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Algebra 1 : Functions and Lines

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Example Questions

Example Question #614 : Equations Of Lines

Find the midpoint of the line segment with these endpoints: (5, 7) and (9, 15) .

Possible Answers:

(8, 12)

(4, 8)

(7, 11)

(14, 22)

Correct answer:

(7, 11)

Explanation:

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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Example Question #861 : Functions And Lines

What is the midpoint of the points (-2,3) and (1,2) ?

Possible Answers:

$\left(\frac{1}{2},\frac{5}{2}\right)$

$\left(-\frac{5}{2},\frac{1}{2}\right)$

$\left(-\frac{1}{2},\frac{5}{2}\right)$

$\left(-\frac{1}{2},-\frac{5}{2}\right)$

$\left(\frac{1}{2},-\frac{5}{2}\right)$

Correct answer:

$\left(-\frac{1}{2},\frac{5}{2}\right)$

Explanation:

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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Example Question #22 : How To Find The Midpoint Of A Line Segment

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

Possible Answers:

$\small (9,5)$

(9,1)

$\small (6,2)$

$\small \small (6,5)$

Correct answer:

$\small \small (6,5)$

Explanation:

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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Example Question #36 : Midpoint Formula

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

Possible Answers:

$\small (0,-8)$

$\small (10, 2)$

$\small \small (2, -10)$

$\small (-10,2)$

Correct answer:

$\small (-10,2)$

Explanation:

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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Example Question #22 : How To Find The Midpoint Of A Line Segment

Find the midpoint of a line containing the points (-2,2) and (2,4) .

Possible Answers:

(-2,0)

(-2,-4)

(0,3)

(0,2)

(3,0)

Correct answer:

(0,3)

Explanation:

Use the midpoint formula:

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

Remember points are written in the following format:

(x,y)

Substitute.

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

Simplify.

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

(0,3)

Our midpoint is (0,3) .

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Example Question #23 : How To Find The Midpoint Of A Line Segment

What is the midpoint of the coordinates (-3,7) and (4,0) ?

Possible Answers:

(0, 0)

(3.5, 0.5)

(-1.5, 0.5)

(0.5, 3.5)

(2, 2)

Correct answer:

(0.5, 3.5)

Explanation:

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

(-3,7)=(x_1, y_1) and (4,0)=(x_2+y_2)

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

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Example Question #31 : How To Find The Midpoint Of A Line Segment

Find the midpoint between the given points:

$(5,-2),\: (-3,7)$

Possible Answers:

$\left(6,-\frac{5}{2}\right)$

$\left(1,\frac{5}{2}\right)$

$\left(\frac{3}{2},2\right)$

(2,5)

Correct answer:

$\left(1,\frac{5}{2}\right)$

Explanation:

Using the midpoint formula:

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

Plugging in our points

$(5,-2)=(x_1,y_1),\: (-3,7)=(x_2,y_2)$

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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Example Question #31 : How To Find The Midpoint Of A Line Segment

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

Possible Answers:

(5, 4)

$\left(\frac{9}{2}, \frac{15}{2}\right)$

(2, 7)

(4, 5)

Correct answer:

(5, 4)

Explanation:

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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Example Question #32 : How To Find The Midpoint Of A Line Segment

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

Possible Answers:

(2, 1)

(8, 5)

(-5, 8)

(8, 30)

Correct answer:

(-5, 8)

Explanation:

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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Example Question #34 : How To Find The Midpoint Of A Line Segment

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

Possible Answers:

(-2, 6)

$\left(-\frac{3}{2}, 12\right)$

$\left(-\frac{3}{2}, 6\right)$

$\left(-\frac{5}{2}, 4\right)$

Correct answer:

$\left(-\frac{3}{2}, 12\right)$

Explanation:

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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Algebra 1 : Functions and Lines

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #614 : Equations Of Lines

Example Question #861 : Functions And Lines

Example Question #22 : How To Find The Midpoint Of A Line Segment

Example Question #36 : Midpoint Formula

Example Question #22 : How To Find The Midpoint Of A Line Segment

Example Question #23 : How To Find The Midpoint Of A Line Segment

Example Question #31 : How To Find The Midpoint Of A Line Segment

Example Question #31 : How To Find The Midpoint Of A Line Segment

Example Question #32 : How To Find The Midpoint Of A Line Segment

Example Question #34 : How To Find The Midpoint Of A Line Segment

All Algebra 1 Resources

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