Question

the point k lies on the segment jl. find the coordinates of k so that the ratio of jk to kl is 5 to 3. j(-26,14) k(?,?) l(6,-2) coordinates of k: ( )

Explanation:

Step1: Recall section - formula

If a point $K(x,y)$ divides the line - segment joining $J(x_1,y_1)$ and $L(x_2,y_2)$ in the ratio $m:n$, then $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here, $x_1=-26,y_1 = 14,x_2 = 6,y_2=-2,m = 5,n = 3$.

Step2: Calculate the x - coordinate of K

$x=\frac{5\times6+3\times(-26)}{5 + 3}=\frac{30-78}{8}=\frac{-48}{8}=-6$.

Step3: Calculate the y - coordinate of K

$y=\frac{5\times(-2)+3\times14}{5 + 3}=\frac{-10 + 42}{8}=\frac{32}{8}=4$.

Answer:

$(-6,4)$