How to find the midpoint of a line segment - High School Math

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Question

What is the midpoint of a line segment connecting the points and ?

Answer

Use the midpoint formula, $mid=(\frac{x_{1}+x_2}{2}, \frac{y_1+y_2}{2})$ , with our points and .

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

$mid=(\frac{4}{2},\frac{8}{2})=(2,4)$

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Question

What would be the midpoint of a line segment with endpoints at and ?

Answer

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 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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Question

What would be the midpoint of a line segment with endpoints at and ?

Answer

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 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.

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Question

If a line has a midpoint at , and the endpoints are and , what is the value of ?

Answer

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 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.

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

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Question

What is the midpoint of the line segment which connects and ?

Answer

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 .

To find the y-coordinate of our midpoint, we find the average of and , which is .

Thus, our midpoint is

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Question

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

Answer

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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Question

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

Answer

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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Question

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

Answer

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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Question

Find the midpoint of the line segment with end points and .

Answer

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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Question

Find the midpoint between these two points:

and

Answer

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

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

Plug in the given points and simplify:

$(\frac{-12+4}{2},\frac{-1+3}{2})=(-4,1)$

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Question

Find the midpoint of these two points:

and

Answer

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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Question

A line segment has endpoints at and . What is the midpoint of this segment?

Answer

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.

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

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

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

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Question

Find the midpoint of the line segment connecting and .

Answer

To find the midpoint of a line segment, we find the average of the -values and the average of the -values. Thus, we have that:

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

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Question

What is the midpoint of a line segment whose endpoints are ?

Answer

The midpoint is the average of the endpoints.

$(\frac{3-1}{2}, \frac{11-7}{2})=(\frac{2}{2},\frac{4}{2})=(1,2)$

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