Question

the point k lies on the segment $overline{jl}$. find the coordinates of k so that jk is $\frac{5}{7}$ of jl. j (-29, -12) l (6, 2) k (?,?)

Explanation:

Step1: Use the section - formula

The section - formula for a point \(K(x,y)\) that divides the line segment joining \(J(x_1,y_1)\) and \(L(x_2,y_2)\) in the ratio \(m:n\) is given by \(x=\frac{mx_2+nx_1}{m + n}\) and \(y=\frac{my_2+ny_1}{m + n}\). Here, \(m = 5\), \(n=7 - 5=2\), \(x_1=-29\), \(y_1=-12\), \(x_2 = 6\), and \(y_2=2\).

Step2: Calculate the x - coordinate of \(K\)

\[x=\frac{5\times6+2\times(-29)}{5 + 2}=\frac{30-58}{7}=\frac{-28}{7}=-4\]

Step3: Calculate the y - coordinate of \(K\)

\[y=\frac{5\times2+2\times(-12)}{5 + 2}=\frac{10 - 24}{7}=\frac{-14}{7}=-2\]

Answer:

\((-4,-2)\)