Question

Find the coordinates of a point P on the line segment joining A(1, 2) and B(6, 7) such

that ratio is 2:3​

Answer 1

Answer:

A=(1,2), B=(6,7), P=(x,y)

x1=1, x2=6, y1=2, y2=7, m1=2, m2=3

$x = \frac{m1x2 + m2x1}{m1+ m2} = \frac{2(6) + 3(1)}{2 + 3}= \frac{12 + 3}{5} = \frac{15}{5} = 3$

$y = \frac{m1y2 + m2y1}{m1 + m2} = \frac{2(7) + 3(2)}{2 + 3} = \frac{14 + 6}{5} = \frac{20}{5} = 4$

Therefore, the coordinates of a point P are (3,4).