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 ratio in which the line segment joining the houses B (0,6) and A (6,0) is divided by the house D(3,3).

• A. 1:1
• B. 1:2
• C. 2:1
• D. 2:3

Answer 1

The correct option is A 1:1

Let the ratio in which the line segment joining B (0,6) and A (6,0) is divided by the house D(3,3) be k : 1.
Therefore, $3=\frac{6k+1\left(0\right)}{k+1}$
$\Rightarrow$ $3k+3=6k$
$\Rightarrow$ $3=3k$
$\Rightarrow$ $k=\frac{1}{1}=1$
$\Rightarrow$ $k:1=1:1$
Therefore, the ratio in which the line segment joining the points B (0,6) and A (6,0) is divided is 1:1.