Find the coordinates of the midpoint of the line segment joining the points $(7, - 3)$ and $(- 2, 4)$ .

medium 2 marks Class 5 · Mathematics · Boxes and Sketches

Answer

(\frac{5}{2}, \frac{1}{2})

The correct answer is $(\frac{5}{2}, \frac{1}{2})$ — Therefore the midpoint is $left(\dfrac{5}{2},\dfrac{1}{2}\right)$ .

Step-by-step solution

The midpoint formula for points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ is $M = (\frac{x _{1} + x _{2}}{2},, \frac{y _{1} + y _{2}}{2})$ .
Let $(x_{1}, y_{1}) = (7, - 3)$ and $(x_{2}, y_{2}) = (- 2, 4)$ .
Compute the sum of the x‑coordinates: $7 + (- 2) = 5$ .
Divide by 2 to find the x‑coordinate of the midpoint: $\frac{5}{2} = 2.5$ .
Compute the sum of the y‑coordinates: $- 3 + 4 = 1$ .
Divide by 2 to find the y‑coordinate: $\frac{1}{2} = 0.5$ .
Therefore the midpoint is $left(\dfrac{5}{2},\dfrac{1}{2}\right)$ .

Common mistake: Using average of absolute values or forgetting to divide by 2

Concept tested: Midpoint of a line segment