Algebra - How to find the midpoint of a line segment

Find the midpoint of the line segment that has endpoints at $(7, 0) \text{ and }(8,9)$ .

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

$\left(\frac{1}{2}, -\frac{9}{2}\right)$

$\left(\frac{7}{2}, \frac{17}{2}\right)$

Explanation

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

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

$\text{Midpoint}=\left(\frac{7+8}{2}, \frac{0+9}{2}\right)=\left(\frac{15}{2}, \frac{9}{2}\right)$

Find the midpoint of a line segment with the following endpoints:

Explanation

Finding the midpoint of a line segment only requires that we find the midpoint, or average of both the x and y components. In order to do that, we use the following formula:

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

For the points (2,6) and (12,12) plug in the numbers and solve:

$(\frac{2+12}{2},\frac{6+12}{2})=(\frac{14}{2},\frac{18}{2})=(7,9)$

This gives a final answer of

What is the midpoint of a line segment with the end points and ?

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.

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

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

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

Find the midpoint of the line segment formed by the points

(-1, -3) and (3, 3).

(1, 0)

(2, 0)

(-4, -6)

(1, -1)

(2, 2)

Explanation

To find the midpoint between two points, we use the following formula:

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

where and are the points given. So, given the points

(-1, -3) and (3, 3), we can substitute into the formula.

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

$(\frac{2}{2}, \frac{0}{2})$

Therefore, the midpoint between (-1, -3) and (3, 3) is (1, 0).

Find the point located exactly halfway between the points and

Explanation

Find the point located exactly halfway between the points and

We can find the midpoint of any pair of points via the following:

$M=(\frac{x_2-x_1}{2},\frac{y_2-y_1}{2})$

All we need to do is plug in our given points.

We'll call point 2 and point 1

So,

$M=(\frac{63-9}{2},\frac{43-37}{2})=(\frac{54}{2},\frac{6}{2})=(27,3)$

A line has endpoints of and . What is its midpoint?

Explanation

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

To find the midpoint of and , you simply plug in the points into the midpoint formula: $(\frac{5+-1}{2},\frac{-2+0}{2})$ , which gives you the point .

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

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

Explanation

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

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

$\text{Midpoint}=\left(\frac{1+9}{2}, \frac{3+5}{2}\right)=(5, 4)$

Find the midpoint of the line segment with the following endpoints:

Explanation

Finding the midpoint of a line segment only requires that we find the midpoint, or average of both the x and y components. In order to do that, we use the following formula:

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

For the points (-2,5) and (4,7) plug in the numbers and solve:

$(\frac{-2+4}{2},\frac{5+7}{2})=(\frac{2}{2},\frac{12}{2})=(1,6)$

This gives a final answer of

Find the midpoint of a line segment with and as its endpoints.

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.

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

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

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

Find the midpoint of the line segment with endpoints $\left ( \frac{1}{3}, \frac{5}{6} \right )$ and $\left ( -\frac{5}{6},\frac{2}{3} \right )$ .

$\left ( -\frac{1 }{4}, \frac{3 }{4} \right )$

$\left ( -\frac{1 }{2}, \frac{3 }{2} \right )$

$\left ( \frac{1 }{4}, \frac{3 }{4} \right )$

$\left ( \frac{7 }{12}, -\frac{1 }{12} \right )$

$\left ( -\frac{7 }{12}, \frac{1 }{12} \right )$

Explanation

Use the midpoint formula:

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

Substitute:

$\frac{x_{1}+x_{2}}{2} = \frac{ \frac{1}{3} + \left (-\frac{5}{6} \right )}{2}= \frac{ \frac{2}{6} - \frac{5}{6} }{2}= \frac{-\frac{3}{6}}{2}= \frac{-\frac{1}{2}}{2} = -\frac{1}{2} \div 2 = -\frac{1}{2} \cdot\frac{1}{2} =-\frac{1}{4}$

$\frac{y_{1}+y_{2}}{2} = \frac{ \frac{5}{6} + \frac{2}{3}}{2} = \frac{ \frac{5}{6} + \frac{4}{6}}{2} = \frac{ \frac{9}{6} }{2}= \frac{ \frac{3}{2} }{2} = \frac{3}{2} \div 2 = \frac{3}{2} \cdot \frac{1}{2} = \frac{3}{4}$

The midpoint is $\left ( -\frac{1 }{4}, \frac{3 }{4} \right )$ .

How to find the midpoint of a line segment

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