Question

The coordinates of AB are A(-5, -1) and B(-2, -6). If AC : CB = 3 : 7, what are the coordinates of point C?

Answer 1

$\text{Let the coordinates of AB are }A(-5,-1), \text{ and }B(-2, -6)\\ \\ \text{let the coordinate of th point C be (x, y), such that}\\ \\ AC:CB=3:7\\ \\ \text{By the section formula, we know that if P(x,y) lies on a line segment AB}\\ \text{where, }A(x_1,y_1), \ B(x_2,y_2)\text{ and satisfy the ratio, }AP:PB=m:n, \text{ then}$

$P=\left ( \frac{mx_2+nx_1}{m+n}, \ \frac{my_2+ny_1}{m+n} \right ).\\ \\ \text{So using this formula, we get for the given problem}\\ \\ C=\left ( \frac{3(-2)+7(-5)}{3+7}, \ \frac{3(-6)+7(-1)}{3+7} \right )\\ \\ \Rightarrow C=\left ( \frac{-6-35}{10}, \ \frac{-18-7}{10} \right )\\ \\ \Rightarrow C=\left ( \frac{-41}{10}, \ \frac{-25}{10} \right )\\ \\ \Rightarrow C=\left ( -4.1, \ -2.5 \right )$

Coordinates of the point C is: (-4.1, -2.5)