Question

Find the coordinates of the midpoint of the line segment joining the points (2, 1) and (1, -3).

• A. $(0,\frac{1}{3})$
• B. $(2,\frac{-3}{5})$
• C. $(\frac{3}{2},-1)$
• D. $(\frac{1}{4},0)$

Answer 1

The correct option is C $(\frac{3}{2},-1)$

Let the midpoint be (x, y).

If (x, y) is the midpoint of the line joining the points $(x_1,y_1)\text{and}(x_2,y_2)$ then
$(x,y)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Here, $(x_1,y_1)=(2,1)$,
$(x_2,y_2)=(1,-3)$

$\Rightarrow (x,y)=(\frac{2+1}{2},\frac{1+(-3)}{2})=(\frac{3}{2},-1)$

Therefore, coordinates of the midpoint of the line segment joining the points (2, 1) and (1, -3) are $(\frac{3}{2},-1)$.