Question

Three points are A(6, 3), B(– 3, 5), C(4, – 2) and P (x, y) is a point, then the ratio of area of $\Delta PBC$and $\Delta ABC$is

• A. $\left| \frac{x + y - 2}{7} \right|$
• B. $\left| \frac{x - y + 2}{2} \right|$
• C. $\left| \frac{x - y - 2}{7} \right|$
• D. None

Answer 1

Answer: (A)

$\left| \frac{x + y - 2}{7} \right|$

Answer 2

$\frac{\text{Area of }\Delta PBC}{\text{Area of }\Delta ABC} = \frac{\frac{1}{2}\left\lbrack - 3( - 2 - y) + 4(y - 5) + x(5 + 2) \right\rbrack}{\frac{1}{2}\left\lbrack 6(5 + 2) - 3( - 2 - 3) + 4(3 - 5) \right\rbrack}$=$\left| \frac{7x + 7y - 14}{49} \right| = \left| \frac{x + y - 2}{7} \right|$