Math - How to find the midpoint of a line segment

Find the midpoint of the line segment connecting and .

Explanation

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

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

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 .

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

Thus, our midpoint is

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

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

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

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

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 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.

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

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

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:

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

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

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

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

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:

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

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

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

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

Explanation

The midpoint is the average of the endpoints.

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

Find the midpoint between these two points:

and

Explanation

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:

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

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

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

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

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

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

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:

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

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

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

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

$\left ( 5,6 \right )$

$\left ( 0,6 \right )$

$\left ( 3,6 \right )$

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

$\left ( 6,5 \right )$

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).