DSQ: Calculating the slope of a perpendicular line - GMAT Quantitative

Card 0 of 24

Question

Consider and .

Find the slope of .

I) passes through the point .

II) is perpendicular to .

Answer

We are given a line, f(x), and asked to find the slope of another line, h(x).

I) Gives a point on h(x). We could plug in the point and solve for our slope. When we do this since x=0 we are unable to find the value for our slope. Therefore, statement I is not sufficient to solve the question.

II) Tells us the two lines are perpendicular. Take the opposite reciprocal of the slope of f(x) to find the slope of h(x).

Therefore,

$\f(x): 4y=16x-5 \y=4x-\frac{5}{4} \m=4$

and thus the slope of h(x) will be,

$m_h=-\frac{1}{m_f}=-\frac{1}{4}$ .

Statement II is sufficient to answer the question.

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Question

Calculate the slope of a line perpendicular to line .

Line passes through points and .

The equation for line is .

Answer

Statement 1: We can use the points provided to find the slope of line AB.

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}= \frac{9-5}{1+3}=\frac{4}{4}=1$

Since the slope we're being asked for is of a line perpendicular to line AB, their slopes are inverses of each other.

The slope of our line is then $m=-\frac{1}{m_{AB}}=-\frac{1}{1}=-1$

Statement 2: Since we're provided with the line's equation, we just need to look for the slope.

Where is the slope and is the y-intercept.

In this case, we have so $m_{AB}=1$ . Because our line is perpendicular to line AB, the slope we're looking for is

Compare your answer with the correct one above

Question

Find the slope of a line perpendicular to .

I) passes through the points and .

II) does not pass through the origin.

Answer

Find the slope of a line perpendicular to g(t)

I) g(t) passes through the points (9,6) and (4,-13)

II) g(t) does not pass through the origin

Perpendicular lines have opposite reciprocal slopes. For instance: a line with a slope of $\frac{1}{4}$ would be perpendicular to a line with slope of .

To find the slope of a line, we just need two points.

I) Gives us two points on g(t). We could find the slope of g(t) and then the slope of any line perpendicular to g(t).

$\frac{-13-6}{4-9}=\frac{-19}{-5}=\frac{19}{5}$

So the slope of a line perpendicular to g(t) is equal to:

$\frac{-5}{19}$

II) Is irrelevant or at least not helpful.

Compare your answer with the correct one above

Question

Consider and .

Find the slope of .

I) passes through the point .

II) is perpendicular to .

Answer

We are given a line, f(x), and asked to find the slope of another line, h(x).

I) Gives a point on h(x). We could plug in the point and solve for our slope. When we do this since x=0 we are unable to find the value for our slope. Therefore, statement I is not sufficient to solve the question.

II) Tells us the two lines are perpendicular. Take the opposite reciprocal of the slope of f(x) to find the slope of h(x).

Therefore,

$\f(x): 4y=16x-5 \y=4x-\frac{5}{4} \m=4$

and thus the slope of h(x) will be,

$m_h=-\frac{1}{m_f}=-\frac{1}{4}$ .

Statement II is sufficient to answer the question.

Compare your answer with the correct one above

Question

Calculate the slope of a line perpendicular to line .

Line passes through points and .

The equation for line is .

Answer

Statement 1: We can use the points provided to find the slope of line AB.

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}= \frac{9-5}{1+3}=\frac{4}{4}=1$

Since the slope we're being asked for is of a line perpendicular to line AB, their slopes are inverses of each other.

The slope of our line is then $m=-\frac{1}{m_{AB}}=-\frac{1}{1}=-1$

Statement 2: Since we're provided with the line's equation, we just need to look for the slope.

Where is the slope and is the y-intercept.

In this case, we have so $m_{AB}=1$ . Because our line is perpendicular to line AB, the slope we're looking for is

Compare your answer with the correct one above

Question

Find the slope of a line perpendicular to .

I) passes through the points and .

II) does not pass through the origin.

Answer

Find the slope of a line perpendicular to g(t)

I) g(t) passes through the points (9,6) and (4,-13)

II) g(t) does not pass through the origin

Perpendicular lines have opposite reciprocal slopes. For instance: a line with a slope of $\frac{1}{4}$ would be perpendicular to a line with slope of .

To find the slope of a line, we just need two points.

I) Gives us two points on g(t). We could find the slope of g(t) and then the slope of any line perpendicular to g(t).

$\frac{-13-6}{4-9}=\frac{-19}{-5}=\frac{19}{5}$

So the slope of a line perpendicular to g(t) is equal to:

$\frac{-5}{19}$

II) Is irrelevant or at least not helpful.

Compare your answer with the correct one above

Question

Consider and .

Find the slope of .

I) passes through the point .

II) is perpendicular to .

Answer

We are given a line, f(x), and asked to find the slope of another line, h(x).

I) Gives a point on h(x). We could plug in the point and solve for our slope. When we do this since x=0 we are unable to find the value for our slope. Therefore, statement I is not sufficient to solve the question.

II) Tells us the two lines are perpendicular. Take the opposite reciprocal of the slope of f(x) to find the slope of h(x).

Therefore,

$\f(x): 4y=16x-5 \y=4x-\frac{5}{4} \m=4$

and thus the slope of h(x) will be,

$m_h=-\frac{1}{m_f}=-\frac{1}{4}$ .

Statement II is sufficient to answer the question.

Compare your answer with the correct one above

Question

Calculate the slope of a line perpendicular to line .

Line passes through points and .

The equation for line is .

Answer

Statement 1: We can use the points provided to find the slope of line AB.

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}= \frac{9-5}{1+3}=\frac{4}{4}=1$

Since the slope we're being asked for is of a line perpendicular to line AB, their slopes are inverses of each other.

The slope of our line is then $m=-\frac{1}{m_{AB}}=-\frac{1}{1}=-1$

Statement 2: Since we're provided with the line's equation, we just need to look for the slope.

Where is the slope and is the y-intercept.

In this case, we have so $m_{AB}=1$ . Because our line is perpendicular to line AB, the slope we're looking for is

Compare your answer with the correct one above

Question

Find the slope of a line perpendicular to .

I) passes through the points and .

II) does not pass through the origin.

Answer

Find the slope of a line perpendicular to g(t)

I) g(t) passes through the points (9,6) and (4,-13)

II) g(t) does not pass through the origin

Perpendicular lines have opposite reciprocal slopes. For instance: a line with a slope of $\frac{1}{4}$ would be perpendicular to a line with slope of .

To find the slope of a line, we just need two points.

I) Gives us two points on g(t). We could find the slope of g(t) and then the slope of any line perpendicular to g(t).

$\frac{-13-6}{4-9}=\frac{-19}{-5}=\frac{19}{5}$

So the slope of a line perpendicular to g(t) is equal to:

$\frac{-5}{19}$

II) Is irrelevant or at least not helpful.

Compare your answer with the correct one above

Question

Consider and .

Find the slope of .

I) passes through the point .

II) is perpendicular to .

Answer

We are given a line, f(x), and asked to find the slope of another line, h(x).

I) Gives a point on h(x). We could plug in the point and solve for our slope. When we do this since x=0 we are unable to find the value for our slope. Therefore, statement I is not sufficient to solve the question.

II) Tells us the two lines are perpendicular. Take the opposite reciprocal of the slope of f(x) to find the slope of h(x).

Therefore,

$\f(x): 4y=16x-5 \y=4x-\frac{5}{4} \m=4$

and thus the slope of h(x) will be,

$m_h=-\frac{1}{m_f}=-\frac{1}{4}$ .

Statement II is sufficient to answer the question.

Compare your answer with the correct one above

Question

Calculate the slope of a line perpendicular to line .

Line passes through points and .

The equation for line is .

Answer

Statement 1: We can use the points provided to find the slope of line AB.

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}= \frac{9-5}{1+3}=\frac{4}{4}=1$

Since the slope we're being asked for is of a line perpendicular to line AB, their slopes are inverses of each other.

The slope of our line is then $m=-\frac{1}{m_{AB}}=-\frac{1}{1}=-1$

Statement 2: Since we're provided with the line's equation, we just need to look for the slope.

Where is the slope and is the y-intercept.

In this case, we have so $m_{AB}=1$ . Because our line is perpendicular to line AB, the slope we're looking for is

Compare your answer with the correct one above

Question

Find the slope of a line perpendicular to .

I) passes through the points and .

II) does not pass through the origin.

Answer

Find the slope of a line perpendicular to g(t)

I) g(t) passes through the points (9,6) and (4,-13)

II) g(t) does not pass through the origin

Perpendicular lines have opposite reciprocal slopes. For instance: a line with a slope of $\frac{1}{4}$ would be perpendicular to a line with slope of .

To find the slope of a line, we just need two points.

I) Gives us two points on g(t). We could find the slope of g(t) and then the slope of any line perpendicular to g(t).

$\frac{-13-6}{4-9}=\frac{-19}{-5}=\frac{19}{5}$

So the slope of a line perpendicular to g(t) is equal to:

$\frac{-5}{19}$

II) Is irrelevant or at least not helpful.

Compare your answer with the correct one above

Question

Consider and .

Find the slope of .

I) passes through the point .

II) is perpendicular to .

Answer

We are given a line, f(x), and asked to find the slope of another line, h(x).

I) Gives a point on h(x). We could plug in the point and solve for our slope. When we do this since x=0 we are unable to find the value for our slope. Therefore, statement I is not sufficient to solve the question.

II) Tells us the two lines are perpendicular. Take the opposite reciprocal of the slope of f(x) to find the slope of h(x).

Therefore,

$\f(x): 4y=16x-5 \y=4x-\frac{5}{4} \m=4$

and thus the slope of h(x) will be,

$m_h=-\frac{1}{m_f}=-\frac{1}{4}$ .

Statement II is sufficient to answer the question.

Compare your answer with the correct one above

Question

Calculate the slope of a line perpendicular to line .

Line passes through points and .

The equation for line is .

Answer

Statement 1: We can use the points provided to find the slope of line AB.

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}= \frac{9-5}{1+3}=\frac{4}{4}=1$

Since the slope we're being asked for is of a line perpendicular to line AB, their slopes are inverses of each other.

The slope of our line is then $m=-\frac{1}{m_{AB}}=-\frac{1}{1}=-1$

Statement 2: Since we're provided with the line's equation, we just need to look for the slope.

Where is the slope and is the y-intercept.

In this case, we have so $m_{AB}=1$ . Because our line is perpendicular to line AB, the slope we're looking for is

Compare your answer with the correct one above

Question

Find the slope of a line perpendicular to .

I) passes through the points and .

II) does not pass through the origin.

Answer

Find the slope of a line perpendicular to g(t)

I) g(t) passes through the points (9,6) and (4,-13)

II) g(t) does not pass through the origin

Perpendicular lines have opposite reciprocal slopes. For instance: a line with a slope of $\frac{1}{4}$ would be perpendicular to a line with slope of .

To find the slope of a line, we just need two points.

I) Gives us two points on g(t). We could find the slope of g(t) and then the slope of any line perpendicular to g(t).

$\frac{-13-6}{4-9}=\frac{-19}{-5}=\frac{19}{5}$

So the slope of a line perpendicular to g(t) is equal to:

$\frac{-5}{19}$

II) Is irrelevant or at least not helpful.

Compare your answer with the correct one above

Question

Consider and .

Find the slope of .

I) passes through the point .

II) is perpendicular to .

Answer

We are given a line, f(x), and asked to find the slope of another line, h(x).

I) Gives a point on h(x). We could plug in the point and solve for our slope. When we do this since x=0 we are unable to find the value for our slope. Therefore, statement I is not sufficient to solve the question.

II) Tells us the two lines are perpendicular. Take the opposite reciprocal of the slope of f(x) to find the slope of h(x).

Therefore,

$\f(x): 4y=16x-5 \y=4x-\frac{5}{4} \m=4$

and thus the slope of h(x) will be,

$m_h=-\frac{1}{m_f}=-\frac{1}{4}$ .

Statement II is sufficient to answer the question.

Compare your answer with the correct one above

Question

Calculate the slope of a line perpendicular to line .

Line passes through points and .

The equation for line is .

Answer

Statement 1: We can use the points provided to find the slope of line AB.

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}= \frac{9-5}{1+3}=\frac{4}{4}=1$

Since the slope we're being asked for is of a line perpendicular to line AB, their slopes are inverses of each other.

The slope of our line is then $m=-\frac{1}{m_{AB}}=-\frac{1}{1}=-1$

Statement 2: Since we're provided with the line's equation, we just need to look for the slope.

Where is the slope and is the y-intercept.

In this case, we have so $m_{AB}=1$ . Because our line is perpendicular to line AB, the slope we're looking for is

Compare your answer with the correct one above

Question

Find the slope of a line perpendicular to .

I) passes through the points and .

II) does not pass through the origin.

Answer

Find the slope of a line perpendicular to g(t)

I) g(t) passes through the points (9,6) and (4,-13)

II) g(t) does not pass through the origin

Perpendicular lines have opposite reciprocal slopes. For instance: a line with a slope of $\frac{1}{4}$ would be perpendicular to a line with slope of .

To find the slope of a line, we just need two points.

I) Gives us two points on g(t). We could find the slope of g(t) and then the slope of any line perpendicular to g(t).

$\frac{-13-6}{4-9}=\frac{-19}{-5}=\frac{19}{5}$

So the slope of a line perpendicular to g(t) is equal to:

$\frac{-5}{19}$

II) Is irrelevant or at least not helpful.

Compare your answer with the correct one above

Question

Consider and .

Find the slope of .

I) passes through the point .

II) is perpendicular to .

Answer

We are given a line, f(x), and asked to find the slope of another line, h(x).

I) Gives a point on h(x). We could plug in the point and solve for our slope. When we do this since x=0 we are unable to find the value for our slope. Therefore, statement I is not sufficient to solve the question.

II) Tells us the two lines are perpendicular. Take the opposite reciprocal of the slope of f(x) to find the slope of h(x).

Therefore,

$\f(x): 4y=16x-5 \y=4x-\frac{5}{4} \m=4$

and thus the slope of h(x) will be,

$m_h=-\frac{1}{m_f}=-\frac{1}{4}$ .

Statement II is sufficient to answer the question.

Compare your answer with the correct one above

Question

Calculate the slope of a line perpendicular to line .

Line passes through points and .

The equation for line is .

Answer

Statement 1: We can use the points provided to find the slope of line AB.

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}= \frac{9-5}{1+3}=\frac{4}{4}=1$

Since the slope we're being asked for is of a line perpendicular to line AB, their slopes are inverses of each other.

The slope of our line is then $m=-\frac{1}{m_{AB}}=-\frac{1}{1}=-1$

Statement 2: Since we're provided with the line's equation, we just need to look for the slope.

Where is the slope and is the y-intercept.

In this case, we have so $m_{AB}=1$ . Because our line is perpendicular to line AB, the slope we're looking for is

Compare your answer with the correct one above

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