Question

the point q lies on the segment $overline{pr}$. find the coordinates of q so that the ratio of pq to qr is 4 to 5. p (-19, 12) q (?,?) r (8, -6) coordinates of q :

Explanation:

Step1: Recall section - formula

The formula for the coordinates of a point $Q(x,y)$ that divides the line - segment joining $P(x_1,y_1)$ and $R(x_2,y_2)$ in the ratio $m:n$ is $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here, $x_1=-19,y_1 = 12,x_2 = 8,y_2=-6,m = 4,n = 5$.

Step2: Calculate the x - coordinate of Q

$x=\frac{4\times8+5\times(-19)}{4 + 5}=\frac{32-95}{9}=\frac{-63}{9}=-7$.

Step3: Calculate the y - coordinate of Q

$y=\frac{4\times(-6)+5\times12}{4 + 5}=\frac{-24 + 60}{9}=\frac{36}{9}=4$.

Answer:

$(-7,4)$