Question

The houses of 4 friends are located at the points (6, 6), (0, 6), (3, 3) and (6, 0) as shown in the figure. A, C and B are the vertices of a right triangle. Find the coordinates of the midpoint of the line segment joining the houses A (6,0) and C (6,6).

• A. (2,3)
• B. (6,3)
• C. (3,2)
• D. (3,6)

Answer 1

The correct option is B (6,3)

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, $(x_1,y_1)=(6,0)$,
$(x_2,y_2)=(6,6)$

$\Rightarrow (x,y)=(\frac{6+6}{2},\frac{0+6}{2})=(6,3)$

Therefore, coordinates of the midpoint of the line segment joining the houses A (6,0) and C (6,6) are $(6,3)$.