Question

the point q lies on the segment pr. find the coordinates of q so that the ratio of pq to qr is 4 to 1. p (-1,3) r (9,-12) 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, $P(-1,3)$, $R(9,-12)$, and $m = 4$, $n = 1$.

Step2: Calculate the x - coordinate of Q

Substitute $x_1=-1$, $x_2 = 9$, $m = 4$, and $n = 1$ into the formula for $x$:
$x=\frac{4\times9+1\times(-1)}{4 + 1}=\frac{36-1}{5}=\frac{35}{5}=7$.

Step3: Calculate the y - coordinate of Q

Substitute $y_1 = 3$, $y_2=-12$, $m = 4$, and $n = 1$ into the formula for $y$:
$y=\frac{4\times(-12)+1\times3}{4 + 1}=\frac{-48 + 3}{5}=\frac{-45}{5}=-9$.

Answer:

$(7,-9)$