Question

solve this question please!!!

Answer 1

Answer:

Hello.

Hope this helps.

Since the triangles have the same base BC, the ratio of their area is just the ratio of their heights from BC:

Area(PBC) / Area(ABC)

= ( distance of P from BC ) / ( distance of A from BC ).

So we need to find the distance from a point (x,y) to the line BC.

B = (-5, 3) and C = (2, -4)

The line BC is

( y - 3 ) / ( x + 5 ) = ( -4 - 3 ) / ( 2 + 5) = -1

=> y - 3 = -x - 5

=> x + y + 2 = 0.

The distance from a point (x,y) to the line BC is then

| x + y + 2 | / √(1² + 1²)  =  | x + y + 2 | / √2

Using this, the distance from A = (5, 1) to line BC is

| 5 + 1 + 2 | / √2  =  7 / √2

Therefore

Area(PBC) / Area(ABC)

= ( distance of P from BC ) / ( distance of A from BC )

= | x + y + 2 | / 7