Question

The co-ordinates of A, B, C are (6, 3), (-3, 5), (4, - 2) respectively and P is a point (x,y), then find the value of $\frac{\Delta PBC}{\Delta ABC}:$

• A. $\frac{x+y-2}{7}$
• B. $\frac{x-y}{4}$
• C. $\frac{x+y-3}{5}$
• D. none of these

Answer 1

The correct option is A $\frac{x+y-2}{7}$

Area of $\Delta PBC=\frac{1}{2}\left\{\right(5x+3y)+(6-20)+(4y+2x\left)\right\}=\frac{1}{2}(7x+7y-14)=\frac{7}{2}(x+y-2)$
and area of $\Delta ABC=\frac{1}{2}\left\{\right(30+9)+(6-20)+(12+12\left)\right\}=\frac{49}{2}$
Hence $\frac{\Delta PBC}{\Delta ABC}=\frac{x+y-2}{7}$