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 points B(0, 6) and C(6, 6).

• A. $(0,3)$
• B. $(3,6)$
• C. $(6,3)$
• D. $(6,6)$

Answer 1

The correct option is B $(3,6)$

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

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

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