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Algebra 1 : Midpoint Formula

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Example Questions

Example Question #878 : Functions And Lines

Find the midpoint of the line segment with the endpoints $(1, 2)\text{ and }(3, 9)$ .

Possible Answers:

$\left(2, \frac{11}{2}\right)$

$\left(-1, -\frac{7}{2}\right)$

(4, 11)

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

Correct answer:

$\left(2, \frac{11}{2}\right)$

Explanation:

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

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

$\text{Midpoint}=\left(\frac{1+3}{2}, \frac{2+9}{2}\right)=\left(2, \frac{11}{2}\right)$

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Example Question #879 : Functions And Lines

Find the midpoint of the line segment that has endpoints at $(8, 7)\text{ and }(2, 7)$ .

Possible Answers:

(5, 7)

(-5, -7)

(10, 0)

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

Correct answer:

(5, 7)

Explanation:

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

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

$\text{Midpoint}=\left(\frac{8+2}{2}, \frac{7+7}{2}\right)=(5, 7)$

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Example Question #880 : Functions And Lines

Find the midpoint of the given points:

$(3,6) \,and \, (-1,2)$

Possible Answers:

(2,3)

(0,4)

(2,5)

(0,3)

(1,4)

Correct answer:

(1,4)

Explanation:

To solve for the midpoint, we want to plug in our coordinate values into the midpoint formula:

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

$(\frac{-1+3}{2},\frac{2+6}{2})=(\frac{2}{2},\frac{8}{2})=(1,4)$

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Example Question #51 : Midpoint Formula

Find the midpoint of the given set of coordinates:

$(-5,2)\,and\, (3,-4)$

Possible Answers:

(-1,-1)

(1,-3)

(4,-1)

(-2,-2)

(1,3)

Correct answer:

(-1,-1)

Explanation:

To find the midpoint, we must plug in the values for both points into the midpoint formula:

$(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})=(\frac{-5+3}{2},\frac{2+-4}{2})=(\frac{-2}{2},\frac{-2}{2})=(-1,-1)$

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Example Question #882 : Functions And Lines

What is the midpoint of a line segment with the end points (1,2) and (7,8) ?

Possible Answers:

(5,4)

(-5,-4)

(2,1)

(3,3)

(4,5)

Correct answer:

(4,5)

Explanation:

In order to solve for the midpoint of a line segment when the end points are given, the x and y values must be averaged.

A formula for this would be:
$midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

This probem may be quickly solved for by substituting in the given information.

$midpoint=(\frac{1+7}{2},\frac{2+8}{2})$

$midpoint=(\frac{8}{2},\frac{10}{2})$

$midpoint={\color{Blue} (4,5)}$

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Example Question #882 : Functions And Lines

Find the midpoint of a line segment with (0,0) and (10,4) as its endpoints.

Possible Answers:

(5,4)

(5,2)

(-5,-2)

(2,5)

(-5,-4)

Correct answer:

(5,2)

Explanation:

In order to solve for the midpoint of a line segment when the end points are given, the x and y values must be averaged.

A formula for this would be:
$midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

This probem may be quickly solved for by substituting in the given information.

$midpoint=(\frac{0+10}{2},\frac{0+4}{2})$

$midpoint=(\frac{10}{2},\frac{4}{2})$

$midpoint={\color{Blue} (5,2)}$

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Example Question #884 : Functions And Lines

A line segment has the endpoints (20,40) and (100,26) . What's the midpoint of the line segment?

Possible Answers:

(33,60)

(60,33)

(120,66)

(80,72)

(60,43)

Correct answer:

(60,33)

Explanation:

In order to solve for the midpoint of a line segment when the end points are given, the x and y values must be averaged.

A formula for this would be:
$midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

This probem may be quickly solved for by substituting in the given information.

$midpoint=(\frac{20+100}{2},\frac{40+26}{2})$

$midpoint=(\frac{120}{2},\frac{66}{2})$

$midpoint={\color{Blue} (60,33)}$

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Example Question #885 : Functions And Lines

What is the midpoint of a line segment AB is A is at (3,4) and B is at (17,2) ?

Possible Answers:

(10,5)

(13,7)

(7,-2)

(10,3)

(-7,2)

Correct answer:

(10,3)

Explanation:

This kind of problem can be quickly solved for by using the midpoint formula:

$\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$ where (x₁,y₁) and (x₂,y₂). Either of the endpoints may be assigned as either coordinate point.

Substituting in the information,

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

$\left(\frac{3+17}{2}, \frac{4+2}{2}\right)$

$\left(\frac{20}{2}, \frac{6}{2}\right)$

${\color{Blue} (10,3)}$

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Example Question #886 : Functions And Lines

Find the midpoint of a line segment with the endpoints $\small (-3,-12)$ and $\small (27,-30)$ .

Possible Answers:

$\small (-15,9)$

$\small (15,-9)$

$\small (-12,-21)$

$\small (16,10)$

$\small (12,-21)$

Correct answer:

$\small (12,-21)$

Explanation:

This kind of problem can be quickly solved for by using the midpoint formula:

$\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$ where $\small (x_1,y_1)$ and $\small (x_2,y_2)$ . Either of the endpoints may be assigned as either coordinate point.

Substituting in the information,

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

$\left(\frac{-3+27}{2}, \frac{-30-12}{2}\right)$

$\left(\frac{24}{2}, \frac{-42}{2}\right)$

${\color{Blue} (12,-21)}$

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Example Question #9 : Midpoint Formula

What is the midpoint of a line that connects the points (1,5) and (-7,9) ?

Possible Answers:

(-3,7)

(-3,2)

(-4,7)

(-4,-2)

(4,2)

Correct answer:

(-3,7)

Explanation:

The midpoint formula is $\left(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2}\right)$ .

Therefore, all we need to do is plug in the points given to us to find the midpoint.

In this case, $x_{1}=1,x_{2}=-7,y_{1}=5,y_{2}=9$ .

To find the -value for the midpoint, we add: 1+(-7)=1-7=-6 . Then we divide by : -6/2=-3 .

To find the -value for the midpoint, we add: 5+9=14 . Then we divide by : 14/2=7 .

So our solution is (-3,7) .

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Algebra 1 : Midpoint Formula

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #878 : Functions And Lines

Example Question #879 : Functions And Lines

Example Question #880 : Functions And Lines

Example Question #51 : Midpoint Formula

Example Question #882 : Functions And Lines

Example Question #882 : Functions And Lines

Example Question #884 : Functions And Lines

Example Question #885 : Functions And Lines

Example Question #886 : Functions And Lines

Example Question #9 : Midpoint Formula

All Algebra 1 Resources

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