How to find the midpoint of a line segment - Math

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Question

What is the midpoint of the line segment between points and ?

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Answer

$($\frac{x_1+x_2}{2}$, $\frac{y_1+y_2}{2}$)$ is the midpoint formula and will give the midpoint coordinates.

Plug in the numbers from the given ordered pairs:

$($\frac{1+(-7)}{2}$,$\frac{8+10}{2}$)$

$($\frac{-6}{2}$,$\frac{18}{2}$)$

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Question

Find the midpoint on the line segment from (2, 3) to (4, 1).

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Answer

By using the midpoint formula, we can find the x and y coodinantes fo the midpoint.

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

$$\frac{x_1+x_2}{2}$=\frac{2+4}{2}$=\frac{6}{2}$=3$

$$\frac{y_1+y_2}{2}$=\frac{3+1}{2}$=\frac{4}{2}$=2$

Our coordinates are (3, 2).

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Question

A line is drawn from (2,4) to (8,28). What are the coordinates of its midpoint?

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Answer

The length to the midpoint is the difference between the two points divided by two. That number must then be added to the point:

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Question

Point X (2, 9) and Point Y (8, 3) are endpoints on a line segment. What is the Midpoint M of that line segment?

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Answer

To find the midpoint of a line segment, you add together the components and divide by two ( $\frac{2+8}{2}$ = 5) , do the same for ( $\frac{3+9}{2}$ =6). The answer is (5, 6).

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Question

Find the midpoint that falls between and .

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Answer

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

When we plug in our points, we get $\left ( $\frac{14}{2}$, $\frac{-4}{2}\right)$ .

So, our final answer is .

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Question

What is the midpoint of the points (3,12) and (9,15)?

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Answer

To find the midpoint we must know the midpoint formula which is

We then take the -coordinate from the first point and plug it into the formula as .

We take the -coordinate from the second point and plug it into the formula as .

We then do the same for and .

With all of the points plugged in our equation will look like this.

$($\frac{3+9}{2}$,$\frac{12+15}{2}$)$

We then perform the necessary addition and division to get the answer of

$($\frac{12}{2}$,$\frac{27}{2}$)=(6,13.5)$

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Question

A line segment begins at and ends at the point . What is the location of its midpoint?

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Answer

The difference in -values is 14 and the difference in -values is 8. The midpoint therefore differs by values of 7 and 4 from either of the endpoints.

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Question

Find the midpoint of the line segment that connects the two points below.

Point 1:

Point 2:

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Answer

The average of the the -coordinates and the average of the y-coordinates of the given points will give you the mid-point of the line that connects the points.

$\textup{midpoint}=($\frac{x_1+x_2}{2}$,$\frac{y_1+y_2}{2}$)$ , where is and is .

$($\frac{(0)+(-2)}{2}$, $\frac{(-3)+(4)}{2}$)$

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

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

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Question

$\textup{Two points }S\left ( 5,2\right )\textup{ and }T\left ( -3,10\right )\textup{ lie in the }xy\textup{-coordinate plane.}$

$\textup{What is the midpoint of line segment }$\overline{ST}$\textup{ ?}$

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Answer

$\textup{The coordinates of the midpoint are the averages of the other points' coordinates.}$

$x\textup{-coordinate}=\frac{5+\left ( -3)\right )}{2}$=1;;;;y\textup{-coordinate}=\frac{2+10}{2}$=6$

$\textup{The midpoint is at }\left (1,6\right )$

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Question

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

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Answer

The midpoint formula is

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 .

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Question

A line has endpoints of $\left ( 10,-2 \right )$ and $\left ( -4,8 \right )$ . What is its midpoint?

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Answer

You can find the midpoint of the line by using the midpoint formula: . Plug the endpoints into the formula to get $($\frac{10+-4}{2}$,$\frac{{-2}$+8}{2})$ , or .

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Question

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

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Answer

To find the midpoint, use the midpoint formula: . Plug in the two ordered pairs to the formula to get: $($\frac{-10+4}{2}$,$\frac{14+2}{2}$)$ . Doing this will give you a solution of .

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Question

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

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Answer

To find the midpoint, you can use the midpoint formula: .

Plug in and into the formula: $($\frac{9+-1}{2}$,$\frac{-3+5}{2}$)$ to get .

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Question

A line segment on the coordinate plane has endpoints and . Which quadrant or axis contains its midpoint?

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Answer

The -coordinate of the midpoint is

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

which is negative.

The -coordinate of the midpoint is

$$\frac{-4+10}{2}$ =3$ ,

which is positive.

Since the midpoint has a negative -coordinate and a positive -coordinate, the midpoint is in Quadrant II.

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Question

A line segment on the coordinate plane has endpoints and . Which quadrant or axis contains its midpoint?

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Answer

The -coordinate of the midpoint is

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

which is positive.

The -coordinate of the midpoint is

$\frac{-4+7}{2}$ = $\frac{3}{2}$ ,

which is positive.

Since both coordinates are positive, the midpoint is in Quadrant I.

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Question

Determine the midpoint between the points and

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Answer

To find the midpoint you are actually finding the average of the two values and the average of the two values.

Midpoint formula:

, so we plug our points in to the equation,

$($\frac{-1+(-7)}{2}$, $\frac{5+3}{2}$)$

Simplify and divide

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

Midpoint:

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Question

Find the midpoint of the line segment with endpoints and .

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Answer

Use the midpoint formula:

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

Substitute:

The midpoint is

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Question

Find the midpoint of the line segment with endpoints and .

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Answer

Use the midpoint formula:

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

Substitute:

The midpoint is

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Question

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 )$ .

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Answer

Use the midpoint formula:

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

Substitute:

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

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Question

What is the midpoint of a line with endpoints (2,5) and (18,-9)?

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Answer

To find the midpoint of the line, plug the endpoints into the distance formula: . This will give you $($\frac{2+18}{2}$,$\frac{5+-9}{2}$)$ , or a midpoint of .

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