Question

the coordinate of a and b are (-3,3),(12,-7)respectively.p is a point which divides ab in such a way that ap:pb=2:3 .find the coordinate of p

Answer 1

Hope it is helpful
The coordinates of P (3,-1)

Answer 2

A(-3, 3) (x1 y1)
B(12, -7) (x2 y2)
P(x, y)
m1 = 2, m2 = 3

using sectional formula:
$(x \: y) = ( \frac{m1x2 + m2x1}{m1 + m2} \: \frac{m1y2 + m2y1}{m1 + m2} ) \\ \: = ( \frac{2 \times 12 + 3 \times - 3}{2 + 3} \: \frac{2 \times - 7 + 3 \times 3}{2 + 3} ) \\ \: = ( \frac{15}{5} \: \frac{ - 5}{5} ) \\ \: = (3 \: -1)$
coordinates of P are (3, -1)