How to find the midpoint of a line segment - Algebra

Card 0 of 711

Question

Find the midpoint of the line segment with endpoints and .

Answer

Use the midpoint formula:

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

Substitute:

$\frac{x_{1}+x_{2}}{2} =\frac{3.6+7.2}{2} = \frac{10.8}{2} = 5.4$

$\frac{y_{1}+y_{2}}{2}} \right = \frac{9.1+(-1.5)}{2}} = \frac{7.6}{2} = 3.8$

The midpoint is

Compare your answer with the correct one above

Question

Find the midpoint of and .

Answer

Write the formula for the midpoint. The midpoint is an order pair.

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

Substitute the points.

$(x,y) = (\frac{2+ (-1 )}{2},\frac{9+7}{2})$

Simplify the expressions.

$(x,y) = (\frac{1}{2},\frac{16}{2}) = (\frac{1}{2},8)$

The midpoint is located at: $(\frac{1}{2},8)$

Compare your answer with the correct one above

Question

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

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:

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

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

Compare your answer with the correct one above

Question

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

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).

Compare your answer with the correct one above

Question

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

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:

$X_{midpoint}=X_{1}+\frac{\left (X_{2}-X_{1} \right )}{2}=2+\frac{\left (8-2 \right )}{2}=2+\frac{6}{2}=2+3=5$

$Y_{midpoint}=Y_{1}+\frac{\left (Y_{2}-Y_{1} \right )}{2}=4+\frac{\left (28-4 \right )}{2}=4+\frac{24}{2}=4+12=16$

Compare your answer with the correct one above

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?

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).

Compare your answer with the correct one above

Question

Find the midpoint that falls between and .

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 .

Compare your answer with the correct one above

Question

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

Answer

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

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

We then take the -coordinate from the first point and plug it into the formula as $x_{1}$ .

We take the -coordinate from the second point and plug it into the formula as $x_{2}$ .

We then do the same for $y_{1}$ and $y_{2}$ .

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

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

Compare your answer with the correct one above

Question

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

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.

Compare your answer with the correct one above

Question

Determine the midpoint between the points and

Answer

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

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

, 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:

Compare your answer with the correct one above

Question

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

Point 1:

Point 2:

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 .

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

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

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

Compare your answer with the correct one above

Question

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

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

Answer

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

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

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

Compare your answer with the correct one above

Question

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

Answer

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 .

Compare your answer with the correct one above

Question

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

Answer

You can find the midpoint of the line by using the midpoint formula: $(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$ . Plug the endpoints into the formula to get $(\frac{10+-4}{2},\frac{{-2}+8}{2})$ , or .

Compare your answer with the correct one above

Question

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

Answer

To find the midpoint, use the midpoint formula: $(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$ . 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 .

Compare your answer with the correct one above

Question

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

Answer

To find the midpoint, you can use the midpoint formula: $(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$ .

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

Compare your answer with the correct one above

Question

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

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.

Compare your answer with the correct one above

Question

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

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.

Compare your answer with the correct one above

Question

Find the midpoint of the line segment with endpoints and .

Answer

Use the midpoint formula:

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

Substitute:

$\frac{x_{1}+x_{2}}{2} =\frac{1.6+(-1.4)}{2} = \frac{0.2}{2} = 0.1$

$\frac{y_{1}+y_{2}}{2}} \right = \frac{7.3+4.7)}{2}} = \frac{12}{2} = 6$

The midpoint is

Compare your answer with the correct one above

Question

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

Answer

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

Compare your answer with the correct one above

Tap the card to reveal the answer