Question

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the coordinates of the endpoints of $overline{pq}$ are $p(3, 5)$ and $q(18, 15)$. point $r$ is on $overline{pq}$ and divides it such that $pr:qr$ is $1:4$. what are the coordinates of $r$? write your answers as integers or decimals.

Explanation:

Step1: Recall section - formula

If a point $R(x,y)$ divides the line - segment joining $P(x_1,y_1)$ and $Q(x_2,y_2)$ in the ratio $m:n$, then $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here, $x_1 = 3,y_1 = 5,x_2 = 18,y_2 = 15,m = 1,n = 4$.

Step2: Calculate the x - coordinate of R

$x=\frac{1\times18+4\times3}{1 + 4}=\frac{18 + 12}{5}=\frac{30}{5}=6$.

Step3: Calculate the y - coordinate of R

$y=\frac{1\times15+4\times5}{1 + 4}=\frac{15+20}{5}=\frac{35}{5}=7$.

Answer:

$(6,7)$