Question

the point q lies on the segment $overline{pr}$. find the coordinates of q so that the ratio of pq to qr is 1 to 7. p (-30, 22) q (?,?) r (2, -2) coordinates of q:

Explanation:

Step1: Recall section - formula

If a point $Q(x,y)$ divides the line - segment joining $P(x_1,y_1)$ and $R(x_2,y_2)$ in the ratio $m:n$, then $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here, $x_1=-30,y_1 = 22,x_2 = 2,y_2=-2,m = 1,n = 7$.

Step2: Calculate the x - coordinate of Q

$x=\frac{1\times2+7\times(-30)}{1 + 7}=\frac{2-210}{8}=\frac{-208}{8}=-26$.

Step3: Calculate the y - coordinate of Q

$y=\frac{1\times(-2)+7\times22}{1 + 7}=\frac{-2 + 154}{8}=\frac{152}{8}=19$.

Answer:

$(-26,19)$