Question

the point k lies on the segment $overline{jl}$. find the coordinates of k so that the ratio of jk to kl is 5 to 3. j (-6, 3) k (?,?) l (26, -13) coordinates of k : (, )

Explanation:

Step1: Recall the 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, $x_1=-6,y_1 = 3,x_2=26,y_2=-13,m = 5,n = 3$.

Step2: Calculate the x - coordinate of K

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

Step3: Calculate the y - coordinate of K

$y=\frac{5\times(-13)+3\times3}{5 + 3}=\frac{-65 + 9}{8}=\frac{-56}{8}=-7$.

Answer:

$(14,-7)$