Question

the point q lies on the segment $overline{pr}$. find the coordinates of q so that pq is $\frac{2}{9}$ of pr. r (24,32) q (?,?) p (-3,-4) 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, $m = 2$ and $n=9 - 2=7$, $x_1=-3$, $y_1=-4$, $x_2 = 24$, $y_2 = 32$.

Step2: Calculate the x - coordinate of Q

$x=\frac{2\times24+7\times(-3)}{2 + 7}=\frac{48-21}{9}=\frac{27}{9}=3$.

Step3: Calculate the y - coordinate of Q

$y=\frac{2\times32+7\times(-4)}{2 + 7}=\frac{64 - 28}{9}=\frac{36}{9}=4$.

Answer:

$(3,4)$