Geometry - SSAT Upper Level Quantitative

Card 0 of 3420

Question

What is the slope of the given linear equation?

2x + 4y = -7

Answer

We can convert the given equation into slope-intercept form, y=mx+b, where m is the slope. We get y = (-1/2)x + (-7/2)

Compare your answer with the correct one above

Question

Find the slope of the line 6X – 2Y = 14

Answer

Put the equation in slope-intercept form:

y = mx + b

-2y = -6x +14

y = 3x – 7

The slope of the line is represented by M; therefore the slope of the line is 3.

Compare your answer with the correct one above

Question

Can we determine the volume of this shape?

Answer

Volume is a characteristic of three-dimensional shapes. This is a cube, which is a three-dimensional shape. We can think of volume as space within an object or shape, so the volume would be the amount of space inside this cube.

Compare your answer with the correct one above

Question

What is the slope of the line:

$\frac{14}{3}x=\frac{1}{6}y-7$

Answer

First put the question in slope intercept form (y = mx + b):

–(1/6)y = –(14/3)x – 7 =>

y = 6(14/3)x – 7

y = 28x – 7.

The slope is 28.

Compare your answer with the correct one above

Question

If 2x – 4y = 10, what is the slope of the line?

Answer

First put the equation into slope-intercept form, solving for y: 2x – 4y = 10 → –4y = –2x + 10 → y = 1/2*x – 5/2. So the slope is 1/2.

Compare your answer with the correct one above

Question

What is the slope of the line with equation 4_x_ – 16_y_ = 24?

Answer

The equation of a line is:

y = mx + b, where m is the slope

4_x_ – 16_y_ = 24

–16_y_ = –4_x_ + 24

y = (–4_x_)/(–16) + 24/(–16)

y = (1/4)x – 1.5

Slope = 1/4

Compare your answer with the correct one above

Question

The perimeter of an equilateral triangle is 39 meters. In meters, how long is one side of the triangle?

Answer

An equilateral triangle has sides that are the same length. Then, to find the length of one side, you only need to divide the perimeter by 3.

$39\div3=13$

Compare your answer with the correct one above

Question

What is the slope of a line that is parallel to the line 11x + 4y - 2 = 9 – 4x ?

Answer

We rearrange the line to express it in slope intercept form.

Any line parallel to this original line will have the same slope.

$ewline 11x+4y-2=9-4x ewline 4y=11-15x ewline y=\frac{11}{4}-\frac{15}{4}x ewline y=-\frac{15}{4}x+\frac{11}{4}$

Compare your answer with the correct one above

Question

Find the area of a circle with a radius of 4.

Answer

The formula for the area of a circle is as follows:

$A=\Pi\cdot r^{2}$

In this formula, A is area, and r is for radius. We know the radius of the circle is 4, so plug in the numbers to get the answer. Since pi is an irrational constant, it is okay to leave the answer in terms of pi.

$A=\Pi\cdot 4^{2}=16\Pi$

Compare your answer with the correct one above

Question

Find the slope of the line that passes through the points $(2, -3)\text{ and }(-3, -3)$

Answer

Use the following formula to find the slope:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\text{Slope}=\frac{-3-(-3)}{-3-2}=\frac{0}{-5}=0$

Compare your answer with the correct one above

Question

Given the graph of the line below, find the equation of the line.

Answer

To solve this question, you could use two points such as (1.2,0) and (0,-4) to calculate the slope which is 10/3 and then read the y-intercept off the graph, which is -4.

Compare your answer with the correct one above

Question

Define an operation $\wedge$ as follows:

For all complex numbers ,

$a \wedge b = a \div (b+ 2i)$

Evaluate $8 \wedge 4$

Answer

$a \wedge b = a \div (b+ 2i) = \frac{a}{b+2i}$

$8 \wedge 4 = \frac{8}{4+2i}$

Multiply both numerator and denominator by the conjugate of the denominator, , to rationalize the denominator:

$8 \wedge 4 = \frac{8(4-2i)}{(4+2i)(4-2i)}$

$= \frac{8\cdot 4-8\cdot 2i}{4^{2}+2^{2}}$

$= \frac{32-16i}{16+4}$

$= \frac{32-16i}{20}$

$= \frac{32 }{20} - \frac{ 16}{20}i$

$= \frac{8}{5} -\frac{ 4}{5}i$

Compare your answer with the correct one above

Question

Raise to the power of 4.

Answer

$(4i)^{4} = 4^{4} \cdot i ^{4} = 256 \cdot 1 = 256$

Compare your answer with the correct one above

Question

Give the equation of the line through and .

Answer

First, find the slope:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} =\frac{9-1}{2-8}=\frac{8}{-6}=-\frac{4}{3}$

Apply the point-slope formula:

$y-y_{1}= m (x-x_{1})$

$y-1= -\frac{4}{3} (x-8)$

$y-1= -\frac{4}{3} x- \left (-\frac{4}{3} \right )8$

$y-1= -\frac{4}{3} x+ \frac{32}{3}$

$y= -\frac{4}{3} x+ \frac{35}{3}$

Rewriting in standard form:

$\frac{4}{3} x + y= \frac{35}{3}$

Compare your answer with the correct one above

Question

A line can be represented by . What is the slope of the line that is perpendicular to it?

Answer

You will first solve for Y, to get the equation in form.

represents the slope of the line, which would be $-\frac{2}{3}$ .

A perpendicular line's slope would be the negative reciprocal of that value, which is $\frac{3}{2}$ .

Compare your answer with the correct one above

Question

Examine the above diagram. What is ?

Answer

Use the properties of angle addition:

$\left ( x - 13\right )+ (y + 25) +43= 180$

Compare your answer with the correct one above

Question

Give the equation of a line that passes through the point and has an undefined slope.

Answer

A line with an undefined slope has equation for some number ; since this line passes through a point with -coordinate 4, then this line must have equation

Compare your answer with the correct one above

Question

Give the equation of a line that passes through the point and has slope 1.

Answer

We can use the point slope form of a line, substituting $m = 1, x_{1} = 4, y _{1} = 7$ .

$y- y_{1} = m (x-x_{1})$

or

Compare your answer with the correct one above

Question

Find the equation the line goes through the points and .

Answer

First, find the slope of the line.

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}=\frac{2-4}{0-3}=\frac{-2}{-3}=\frac{2}{3}$

Now, because the problem tells us that the line goes through , our y-intercept must be .

Putting the pieces together, we get the following equation:

$y=\frac{2}{3}x+2$

Compare your answer with the correct one above

Question

A line passes through the points and . Find the equation of this line.

Answer

To find the equation of a line, we need to first find the slope.

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}=\frac{-2-6}{-2-(-4)}=\frac{-8}{2}=-4$

Now, our equation for the line looks like the following:

To find the y-intercept, plug in one of the given points and solve for . Using , we get the following equation:

Solve for .

Now, plug the value for into the equation.

Compare your answer with the correct one above

Tap the card to reveal the answer