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High School Math : Midpoint and Distance Formulas

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Example Questions

Example Question #1 : Midpoint And Distance Formulas

What would be the midpoint of a line segment with endpoints at (0,1) and (5,7) ?

Possible Answers:

$(\frac{5}{2},4)$

(1,1)

$(\frac{5}{2},\frac{9}{2})$

$(\frac{5}{2},\frac{5}{2})$

(5,6)

Correct answer:

$(\frac{5}{2},4)$

Explanation:

The midpoint of a line segment is halfway between the two $\small x$ values and halfway between the two $\small y$ values.

Mathematically, that would be the average of each coordinate: $(\frac{x_2+x_1}{2},\frac{y_2+y_1}{2})$ .

Plug in the (x,y) values from the given points and solve.

$(\frac{5+0}{2},\frac{7+1}{2})$

$(\frac{5}{2},\frac{8}{2})$

We can simplify the fraction to give our final answer.

$(\frac{5}{2},4)$

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Example Question #2 : Algebra I

What would be the midpoint of a line segment with endpoints at (1,6) and (9,9) ?

Possible Answers:

(0,0)

(4.5,4.5)

(2.5,7.5)

(5,7.5)

(5,7)

Correct answer:

(5,7.5)

Explanation:

The midpoint of a line segment is halfway between the two $\small x$ values and halfway between the two $\small y$ values.

Mathematically, that would be the average of each coordinate: $(\frac{x_2+x_1}{2},\frac{y_2+y_1}{2})$ .

Plug in the (x,y) values from the given points and solve.

$(\frac{9+1}{2},\frac{9+6}{2})$

$(\frac{10}{2},\frac{15}{2})$

Simplify the fractions to get the final answer.

(5,7.5)

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Example Question #2 : Midpoint And Distance Formulas

If a line has a midpoint at (2,5) , and the endpoints are (0,0) and (4,y) , what is the value of ?

Possible Answers:

2.5

Correct answer:

Explanation:

The midpoint of a line segment is halfway between the two $\small x$ values and halfway between the two $\small y$ values.

Mathematically, that would be the average of the coordinates: $(\frac{x_2+x_1}{2},\frac{y_2+y_1}{2})$ .

Plug in the (x,y) values from the given points.

$(\frac{4+0}{2},\frac{y+0}{2})=(2,5)$

Now we can solve for the missing value.

$(\frac{4}{2},\frac{y}{2})=(2,5)$

$\frac{4}{2}=2$

The $\small x$ values reduce, so both $\small x$ values equal $\small 2$ . Now we need to create a new equation to solve for the $\small y$ value.

$\frac{y}{2}=5$

Multiply both sides by to solve.

$(2)\frac{y}{2}=5(2)$

y=10

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Example Question #3 : Midpoint And Distance Formulas

What is the midpoint of a line segment with endpoints (1,1) and (12,12) ?

Possible Answers:

(6,6)

$(\frac{1}{2},\frac{3}{4})$

$(\frac{13}{2},\frac{13}{2})$

(11,-11)

(13,13)

Correct answer:

$(\frac{13}{2},\frac{13}{2})$

Explanation:

The midpoint formula is this: $(\frac{x_2+x_1}{2},\frac{y_2+y_1}{2})$ .

Plug in the given values from our points and solve:

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

$(\frac{12+1}{2},\frac{12+1}{2})$

$(\frac{13}{2},\frac{13}{2})$

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Example Question #1 : Midpoint And Distance Formulas

What is the midpoint of the line segment with endpoints at (6,3) and (9,2) ?

Possible Answers:

$(\frac{15}{2},\frac{5}{2})$

$(\frac{2}{15},\frac{2}{5})$

$(\frac{2}{3},\frac{5}{3})$

(7,3)

$(\frac{9}{2},\frac{5}{2})$

Correct answer:

$(\frac{15}{2},\frac{5}{2})$

Explanation:

The midpoint formula is this: $(\frac{x_2+x_1}{2},\frac{y_2+y_1}{2})$ .

Plug in the given values from our points and solve:

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

$(\frac{9+6}{2},\frac{2+3}{2})$

$(\frac{15}{2},\frac{5}{2})$

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Example Question #1 : How To Find The Midpoint Of A Line Segment

Find the midpoint between (4, 3) and (6, 9).

Possible Answers:

$\left ( -5,6 \right )$

$\left ( 3,6 \right )$

$\left ( 6,5 \right )$

$\left ( 5,6 \right )$

$\left ( 0,6 \right )$

Correct answer:

$\left ( 5,6 \right )$

Explanation:

Add up the 's and divide in half, which results in 5. Do the same to the 's and you get 6. Put the and in an ordered pair so that your answer is (5, 6).

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Example Question #4 : Midpoint And Distance Formulas

What is the midpoint of the line segment which connects (-6, 8) and (2, 12) ?

Possible Answers:

(-4, 20)

(2, 10)

(-8, -4)

(8, 4)

(-2, 10)

Correct answer:

(-2, 10)

Explanation:

To find the midpoint of a line segment, we find the average of the x and y coordinates of the endpoints. The average of two numbers is the sum of those numbers divided by . Thus, to find the x-coordinate of our midpoint, we find the average of and , and we get (-6+2)/2=-4/2 = -2 .

To find the y-coordinate of our midpoint, we find the average of and , which is (8+12)/2=20/2 = 10 .

Thus, our midpoint is (-2, 10).

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Example Question #3 : Coordinate Geometry

Find the midpoint of the line segment with end points (-2,3) and (-4,16) .

Possible Answers:

(-3,9.5)

(3,9.5)

(3,-9.5)

(6,-19)

(-6,19)

Correct answer:

(-3,9.5)

Explanation:

To find the midpoint of a line segment, use the standard equation:

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

Plugging in the given points:

$(\frac{-2+-4}{2},\frac{3+16}{2})=(-3,9.5)$

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Example Question #5 : Midpoint And Distance Formulas

Find the midpoint of these two points:

(-2,13) and (4,-9)

Possible Answers:

(2,1)

(4,2)

(1,2)

(-1,2)

(2,4)

Correct answer:

(1,2)

Explanation:

The standard formula to find the midpoint of two points is $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$ .

Plug in the given points to find the answer:

$(\frac{-2+4}{2},\frac{13+(-9)}{2})=(\frac{2}{2},\frac{4}{2})=(1,2)$

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Example Question #5 : Midpoint And Distance Formulas

A line segment has endpoints at (2,3) and (-7,3) . What is the midpoint of this segment?

Possible Answers:

(-5,3)

(-4.5,3)

(-4.5,0)

(-2.5,3)

(9,3)

Correct answer:

(-2.5,3)

Explanation:

My midpoint will be at the average of the -values and the average of the -values. Mathematically, $(\frac{x_2+x_1}{2}, \frac{y_2+y_1}{2})$ .

Plug in our given values.

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

$(\frac{-7+2}{2}, \frac{3+3}{2})$

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

(-2.5,3)

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High School Math : Midpoint and Distance Formulas

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : Midpoint And Distance Formulas

Example Question #2 : Algebra I

Example Question #2 : Midpoint And Distance Formulas

Example Question #3 : Midpoint And Distance Formulas

Example Question #1 : Midpoint And Distance Formulas

Example Question #1 : How To Find The Midpoint Of A Line Segment

Example Question #4 : Midpoint And Distance Formulas

Example Question #3 : Coordinate Geometry

Example Question #5 : Midpoint And Distance Formulas

Example Question #5 : Midpoint And Distance Formulas

All High School Math Resources

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