How to find the midpoint of a line

How to Find the Midpoint of a Line?

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Midpoint is a point positioned in between $2$ points and it is in the middle of the line that joins these $2$ points. If the line is drawn to join these \(2 points, the midpoint is a point in the middle of the line and is equal distant from the $2$ points. Presented any $2$ points, say $A$ and $B$ , the midpoint will be a point $M$ which is found halfway in between points $A$ and $B$ . So, to determine the midpoint, you merely measure the length of the line segment and divide it by $2$ .

midpoint of a line

Midpoint Formula used in Math

Presented with $2$ points $A(x_{1},y_{1})$ and $B(x_{2},y_{2})$ , the midpoint in between $A$ and $B$ is given by:

$M(x_{3} \ , \ y_{3}) \ = \ (\frac{x_{1} \ + \ x_{2}}{2} \ , \ \frac{y_{1} \ + \ y_{2}}{2})$

where, $M$ is the midpoint in between $A$ and $B$ , and $(x_{3} \ , \ y_{3})$ are the coordinates.

Free printable Worksheets

Exercises for Finding Midpoint

1) Find the midpoint of the line passing through $(3,-3), (3,7)$ $\ \Rightarrow \$

2) Find the midpoint of the line passing through $(-1,9), (5,-5)$ $\ \Rightarrow \$

3) Find the midpoint of the line passing through $(-4,0), (4,2)$ $\ \Rightarrow \$

4) Find the midpoint of the line passing through $(-4,-5), (-2,5)$ $\ \Rightarrow \$

5) Find the midpoint of the line passing through $(-6,10), (4,-8)$ $\ \Rightarrow \$

6) Find the midpoint of the line passing through $(-6,-4), (2,6)$ $\ \Rightarrow \$

7) Find the midpoint of the line passing through $(-13,7), (7,-5)$ $\ \Rightarrow \$

8) Find the midpoint of the line passing through $(-4,-3), (6,7)$ $\ \Rightarrow \$

9) Find the midpoint of the line passing through $(-5,0), (5,4)$ $\ \Rightarrow \$

10) Find the midpoint of the line passing through $(2,3), (-4,1)$ $\ \Rightarrow \$

Answers

1) Find the midpoint of the line passing through

(3, - 3), (3, 7)

$(3,-3), (3,7)$

\Rightarrow M = (\frac{3 + 3}{2}, \frac{2 + 7}{2})

$\ \Rightarrow \ \color{red}{M = (\frac{3 \ + \ 3}{2}, \frac{2 \ + \ 7}{2})}$

\Rightarrow M = (3, 2)

$\ \Rightarrow \ \color{red}{M = (3, 2)}$

2) Find the midpoint of the line passing through

(- 1, 9), (5, - 5)

$(-1,9), (5,-5)$

\Rightarrow M = (\frac{2 + 5}{2}, \frac{2 + (- 5)}{2})

$\ \Rightarrow \ \color{red}{M = (\frac{2 \ + \ 5}{2}, \frac{2 \ + \ (-5)}{2})}$

\Rightarrow M = (2, 2)

$\ \Rightarrow \ \color{red}{M = (2, 2)}$

3) Find the midpoint of the line passing through

(- 4, 0), (4, 2)

$(-4,0), (4,2)$

\Rightarrow M = (\frac{0 + 4}{2}, \frac{1 + 2}{2})

$\ \Rightarrow \ \color{red}{M = (\frac{0 \ + \ 4}{2}, \frac{1 \ + \ 2}{2})}$

\Rightarrow M = (0, 1)

$\ \Rightarrow \ \color{red}{M = (0, 1)}$

4) Find the midpoint of the line passing through

(- 4, - 5), (- 2, 5)

$(-4,-5), (-2,5)$

\Rightarrow M = (\frac{- 3 + (- 2)}{2}, \frac{0 + 5}{2})

$\ \Rightarrow \ \color{red}{M = (\frac{-3 \ + \ (-2)}{2}, \frac{0 \ + \ 5}{2})}$

\Rightarrow M = (- 3, 0)

$\ \Rightarrow \ \color{red}{M = (-3, 0)}$

5) Find the midpoint of the line passing through

(- 6, 10), (4, - 8)

$(-6,10), (4,-8)$

\Rightarrow M = (\frac{- 1 + 4}{2}, \frac{1 + (- 8)}{2})

$\ \Rightarrow \ \color{red}{M = (\frac{-1 \ + \ 4}{2}, \frac{1 \ + \ (-8)}{2})}$

\Rightarrow M = (- 1, 1)

$\ \Rightarrow \ \color{red}{M = (-1, 1)}$

6) Find the midpoint of the line passing through

(- 6, - 4), (2, 6)

$(-6,-4), (2,6)$

\Rightarrow M = (\frac{- 2 + 2}{2}, \frac{1 + 6}{2})

$\ \Rightarrow \ \color{red}{M = (\frac{-2 \ + \ 2}{2}, \frac{1 \ + \ 6}{2})}$

\Rightarrow M = (- 2, 1)

$\ \Rightarrow \ \color{red}{M = (-2, 1)}$

7) Find the midpoint of the line passing through

(- 13, 7), (7, - 5)

$(-13,7), (7,-5)$

\Rightarrow M = (\frac{- 3 + 7}{2}, \frac{1 + (- 5)}{2})

$\ \Rightarrow \ \color{red}{M = (\frac{-3 \ + \ 7}{2}, \frac{1 \ + \ (-5)}{2})}$

\Rightarrow M = (- 3, 1)

$\ \Rightarrow \ \color{red}{M = (-3, 1)}$

8) Find the midpoint of the line passing through

(- 4, - 3), (6, 7)

$(-4,-3), (6,7)$

\Rightarrow M = (\frac{1 + 6}{2}, \frac{2 + 7}{2})

$\ \Rightarrow \ \color{red}{M = (\frac{1 \ + \ 6}{2}, \frac{2 \ + \ 7}{2})}$

\Rightarrow M = (1, 2)

$\ \Rightarrow \ \color{red}{M = (1, 2)}$

9) Find the midpoint of the line passing through

(- 5, 0), (5, 4)

$(-5,0), (5,4)$

\Rightarrow M = (\frac{0 + 5}{2}, \frac{2 + 4}{2})

$\ \Rightarrow \ \color{red}{M = (\frac{0 \ + \ 5}{2}, \frac{2 \ + \ 4}{2})}$

\Rightarrow M = (0, 2)

$\ \Rightarrow \ \color{red}{M = (0, 2)}$

10) Find the midpoint of the line passing through

(2, 3), (- 4, 1)

$(2,3), (-4,1)$

\Rightarrow M = (\frac{- 1 + (- 4)}{2}, \frac{2 + 1}{2})

$\ \Rightarrow \ \color{red}{M = (\frac{-1 \ + \ (-4)}{2}, \frac{2 \ + \ 1}{2})}$

\Rightarrow M = (- 1, 2)

$\ \Rightarrow \ \color{red}{M = (-1, 2)}$

How to find the midpoint of a line