Question

the point q lies on the segment $overline{pr}$. find the coordinates of q so that the ratio of pq to qr is 5 to 3.
r (26, 13)
q (?,?)
p (-6, -3)
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, $x_1=-6,y_1=-3,x_2 = 26,y_2 = 13,m = 5,n = 3$.

Step2: Calculate the x - coordinate of Q

$x=\frac{5\times26+3\times(-6)}{5 + 3}=\frac{130-18}{8}=\frac{112}{8}=14$.

Step3: Calculate the y - coordinate of Q

$y=\frac{5\times13+3\times(-3)}{5 + 3}=\frac{65 - 9}{8}=\frac{56}{8}=7$.

Answer:

$(14,7)$