Question

1. find the point g on $overline{ab}$ with a (-3, 5) and b (5, 0) such that the ratio of ag to gb is 3:2.

Explanation:

Step1: Recall the section - formula

If a point $G(x,y)$ divides the line - segment joining $A(x_1,y_1)$ and $B(x_2,y_2)$ in the ratio $m:n$, then $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here, $x_1=-3,y_1 = 5,x_2 = 5,y_2 = 0,m = 3,n = 2$.

Step2: Calculate the x - coordinate of point G

$x=\frac{3\times5+2\times(-3)}{3 + 2}=\frac{15-6}{5}=\frac{9}{5}=1.8$.

Step3: Calculate the y - coordinate of point G

$y=\frac{3\times0+2\times5}{3 + 2}=\frac{0 + 10}{5}=2$.

Answer:

The coordinates of point G are $(1.8,2)$.