Functions and Lines - Algebra

Card 0 of 8523

Question

What is the midpoint of a line with endpoints of and ?

Answer

To find the midpoint of the line, plug the endpoints into the midpoint formula, which is

$\left(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2}\right)$

Doing this gives you

$\left(\frac{8+20}{2},\frac{-4+2}{2}\right)$

or

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Question

What is the midpoint of a line segment with endpoints of and ?

Answer

To find the midpoint of the line segment, plug in the endpoints to the midpoint formula, which is

$\left(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2}\right)$

This gives you

$\left(\frac{-7+3}{2},\frac{4+16}{2}\right)$

which equals

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Question

What is the midpoint for the line segment between the points $\left ( -3,7 \right )$ and $\left ( 5,10 \right )\ ?$

Answer

To find the midpoint, use the midpoint formula:

$Midpoint = (\frac{x_{1} + x_{2}}{2}, \frac{y_{1}+y_{2}}{2})$

For this problem, this would be:

$(\frac{-3+5}{2}, \frac{7+10}{2}) = (1, 8.5)$

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Question

Find the midpoint of the line segment with these endpoints: and .

Answer

The midpoint formula is

$\left(\frac{x_{1}+x_{2}}2,\frac{y_{1}+y_2}{2}\right)$ .

Add the two values together and divide the total by two to find the value of the midpoint. Add the two values together and divide the total by two to find the value of the midpoint.

$\ \left(\frac{5+9}2,\frac{7+15}{2}\right)\ \=\left(\frac{14}{2},\frac{22}{2} \right )\ \=(7,11)$

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Question

What is the midpoint of the points and ?

Answer

The midpoint between two points can be found by the equation $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$ . Substiuting in the equation becomes $(\frac{-2+1}{2},\frac{3+2}{2})$ . If you simplfy it the the midpoint is $(-\frac{1}{2},\frac{5}{2})$ .

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Question

Find the midpoint of a line containing the points and .

Answer

Use the midpoint formula:

$\frac{x_{2}+x_{1}}{2}, \frac{y_{2}+y_{1}}{2}$

Remember points are written in the following format:

Substitute.

$\frac{\left ( -2+2 \right )}{2} , \frac{\left ( 2+4 \right )}{2}$

Simplify.

$\frac{\left ( 0 \right )}{2} , \frac{\left ( 6)}{2}$

Our midpoint is .

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Question

What would be the midpoint of a line with endpoints $\small (-3, 6)$ and $\small (15, 4)$ ?

Answer

To find the midpoint, we just need to find the mean of the x-coordinates, and then the mean of the y-coordinates. To find the mean, add the two numbers together and then divide by 2.

Our x-coordinates are -3 and 15.

Their mean is

$\small \frac{-3+15}{2}=\frac{12}{2}=6$ .

Our y-coordinates are 6 and 4.

Their mean is

$\small \frac{6+4}{2}=\frac{10}{2}=5$ .

This gives us a new coordinate pair of $\small (6,5)$ .

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Question

The endpoints of a line segment are $\small (0,0)$ and $\small (-20, 4)$ . What is the midpoint?

Answer

In order to find the midpoint, we have to find the mean of the x-coordinates of the endpoints, and then find the mean of the y-coordinates of the endpoints. To find the mean, add the two numbers together then divide by 2.

The x-coordinates are 0 and -20.

Their mean is

$\small \frac{0 + -20}{2}=\frac{-20}{2}=-10$ .

The y-coordinates are 0 and 4.

Their mean is

$\small \frac{0+4}{2}= \frac{4}{2}= 2$ .

This gives us a new x-, y-coordinate pair of $\small (-10,2)$ .

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Question

What is the midpoint of the coordinates and ?

Answer

The questions is asking for the midpoint of a line between two coordinates.

The midpoint formula is

$\left(\frac{(x_1+x_2)}{2}, \frac{(y_1+y_2)}{2}\right)$ .

Now, fill in the variables to find

and

$\left(\frac{-3+4}{2}, \frac{7+0}{2}\right) = (0.5, 3.5)$

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Question

Find the midpoint between the given points:

Answer

Using the midpoint formula:

$\left(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2}\right)$

Plugging in our points

we can find the midpoint.

$\left(\frac{5-3}{2},\frac{-2+7}{2}\right)=\left(1,\frac{5}{2}\right)$

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Question

Find the midpoint of the line segment that has endpoints at $(7, 0) \text{ and }(8,9)$ .

Answer

To find the midpoint of a line segment, take the average of the x-coordinates and the average of the y-coordinates.

$\text{Midpoint}=\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$

$\text{Midpoint}=\left(\frac{7+8}{2}, \frac{0+9}{2}\right)=\left(\frac{15}{2}, \frac{9}{2}\right)$

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Question

Find the midpoint of the line segment that has endpoints at $(1, 3)\text{ and }(9, 5)$ .

Answer

To find the midpoint of a line segment, take the average of the x-coordinates and the average of the y-coordinates.

$\text{Midpoint}=\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$

$\text{Midpoint}=\left(\frac{1+9}{2}, \frac{3+5}{2}\right)=(5, 4)$

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Question

Find the midpoint of the line segment that has endpoints at $(-2, 6)\text{ and }(-8, 10)$ .

Answer

To find the midpoint of a line segment, take the average of the x-coordinates and the average of the y-coordinates.

$\text{Midpoint}=\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$

$\text{Midpoint}=\left(\frac{-2+(-8)}{2}, \frac{6+10}{2}\right)=(-5, 8)$

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Question

Find the midpoint of a line segment that has endpoints at $\left(\frac{1}{2}, 6\right)$ and $\left(-\frac{7}{2}, 18\right)$ .

Answer

To find the midpoint of a line segment, take the average of the x-coordinates and the average of the y-coordinates.

$\text{Midpoint}=\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$

$\text{Midpoint}=\left(\frac{\frac{1}{2}+(-\frac{7}{2})}{2}, \frac{6+18}{2}\right)=\left(-\frac{3}{2},12\right)$

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Question

Find the midpoint of the line segment that has endpoints at $(100, 5)\text{ and }(2, 0)$ .

Answer

To find the midpoint of a line segment, take the average of the x-coordinates and the average of the y-coordinates.

$\text{Midpoint}=\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$

$\text{Midpoint}=\left(\frac{100+2}{2}, \frac{5+0}{2}\right)=\left(51, \frac{5}{2}\right)$

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Question

Find the midpoint of the line segment that has endpoints at $(-5, -2)\text{ and }(-9, -10)$ .

Answer

To find the midpoint of a line segment, take the average of the x-coordinates and the average of the y-coordinates.

$\text{Midpoint}=\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$

$\text{Midpoint}=\left(\frac{-5+(-9)}{2}, \frac{-2+(-10)}{2}\right)=(-7, -6)$

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Question

Find the midpoint of the line segment that has endpoints at $(1, -2)\text{ and }(7, -12)$ .

Answer

To find the midpoint of a line segment, take the average of the x-coordinates and the average of the y-coordinates.

$\text{Midpoint}=\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$

$\text{Midpoint}=\left(\frac{1+7}{2}, \frac{-2+(-12)}{2}\right)=(4, -7)$

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Question

Find the midpoint of the line segment that has endpoints at $(-0.9, 1)\text{ and }(0.1, 5)$ .

Answer

To find the midpoint of a line segment, take the average of the x-coordinates and the average of the y-coordinates.

$\text{Midpoint}=\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$

$\text{Midpoint}=\left(\frac{-0.9+0.1}{2}, \frac{1+5}{2}\right)=(-0.4, 3)$

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Question

Find the midpoint of a line segment that has endpoints at $(11, -5)\text{ and }(1, -9)$ .

Answer

To find the midpoint of a line segment, take the average of the x-coordinates and the average of the y-coordinates.

$\text{Midpoint}=\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$

$\text{Midpoint}=\left(\frac{11+1}{2}, \frac{-5+(-9)}{2}\right)=(6, -7)$

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Question

Find the midpoint of a line segment that has endpoints at $(-7, 12)\text{ and }(-3, -2)$ .

Answer

To find the midpoint of a line segment, take the average of the x-coordinates and the average of the y-coordinates.

$\text{Midpoint}=\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$

$\text{Midpoint}=\left(\frac{-7+(-3)}{2}, \frac{12+(-2)}{2}\right)=(-5, 5)$

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