Midpoint of a Line Segment Worksheets - Free Printable

I will solve this problem by finding the midpoint of each line segment shown in the image. The midpoint of a line segment is the point that is exactly halfway between the two endpoints. To find it, I can use the midpoint formula: for two points $(x_1, y_1)$ and $(x_2, y_2)$, the midpoint is $\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$. I'll go through each problem one by one.

First, I need to identify the coordinates of the endpoints for each line segment.

Problem 1

- First, look closely: I see a line segment on the first graph. One endpoint appears to be at (-3, 1) and the other at (1, -1).
- Next, find information: I will calculate the midpoint using the formula.
- Then, review the findings: The midpoint is $\left(\frac{-3 + 1}{2}, \frac{1 + (-1)}{2}\right) = \left(\frac{-2}{2}, \frac{0}{2}\right) = (-1, 0)$.

Problem 2

- First, look closely: The line segment goes from (-2, -2) to (4, -2).
- Next, find information: Calculate the midpoint.
- Then, review the findings: The midpoint is $\left(\frac{-2 + 4}{2}, \frac{-2 + (-2)}{2}\right) = \left(\frac{2}{2}, \frac{-4}{2}\right) = (1, -2)$.

Problem 3

- First, look closely: The line segment goes from (1, 3) to (3, -3).
- Next, find information: Calculate the midpoint.
- Then, review the findings: The midpoint is $\left(\frac{1 + 3}{2}, \frac{3 + (-3)}{2}\right) = \left(\frac{4}{2}, \frac{0}{2}\right) = (2, 0)$.

Problem 4

- First, look closely: The line segment goes from (-4, 2) to (0, 2).
- Next, find information: Calculate the midpoint.
- Then, review the findings: The midpoint is $\left(\frac{-4 + 0}{2}, \frac{2 + 2}{2}\right) = \left(\frac{-4}{2}, \frac{4}{2}\right) = (-2, 2)$.

Problem 5

- First, look closely: The line segment goes from (1, 0) to (3, -3).
- Next, find information: Calculate the midpoint.
- Then, review the findings: The midpoint is $\left(\frac{1 + 3}{2}, \frac{0 + (-3)}{2}\right) = \left(\frac{4}{2}, \frac{-3}{2}\right) = (2, -1.5)$.

Problem 6

- First, look closely: The line segment goes from (-2, -2) to (3, 3).
- Next, find information: Calculate the midpoint.
- Then, review the findings: The midpoint is $\left(\frac{-2 + 3}{2}, \frac{-2 + 3}{2}\right) = \left(\frac{1}{2}, \frac{1}{2}\right) = (0.5, 0.5)$.

Problem 7

- First, look closely: The line segment goes from (0, -2) to (2, -4).
- Next, find information: Calculate the midpoint.
- Then, review the findings: The midpoint is $\left(\frac{0 + 2}{2}, \frac{-2 + (-4)}{2}\right) = \left(\frac{2}{2}, \frac{-6}{2}\right) = (1, -3)$.

Problem 8

- First, look closely: The line segment goes from (-3, 0) to (1, -4).
- Next, find information: Calculate the midpoint.
- Then, review the findings: The midpoint is $\left(\frac{-3 + 1}{2}, \frac{0 + (-4)}{2}\right) = \left(\frac{-2}{2}, \frac{-4}{2}\right) = (-1, -2)$.

Problem 9

- First, look closely: The line segment goes from (-2, 1) to (2, -1).
- Next, find information: Calculate the midpoint.
- Then, review the findings: The midpoint is $\left(\frac{-2 + 2}{2}, \frac{1 + (-1)}{2}\right) = \left(\frac{0}{2}, \frac{0}{2}\right) = (0, 0)$.

Now I have found the midpoint for each line segment. I will summarize the answers below.

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Final Answer:

Here are the midpoints for each line segment:

1) $(-1, 0)$
2) $(1, -2)$
3) $(2, 0)$
4) $(-2, 2)$
5) $(2, -1.5)$
6) $(0.5, 0.5)$
7) $(1, -3)$
8) $(-1, -2)$
9) $(0, 0)$