Question

find the coordinates of point k on (overline{jl}) such that the ratio of (jk) to (jl) is (1:4). (j(-5, - 9)) (l(-6, - 10)) show your work here

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, \(J(-5,-9)\), \(L(-6,-10)\), \(m = 1\), and \(n=3\) (since the ratio of \(JK\) to \(JL\) is \(1:4\), so the ratio of \(JK\) to \(KL\) is \(1:3\)).

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

\(x=\frac{1\times(-6)+3\times(-5)}{1 + 3}=\frac{-6-15}{4}=\frac{-21}{4}=-5.25\)

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

\(y=\frac{1\times(-10)+3\times(-9)}{1 + 3}=\frac{-10 - 27}{4}=\frac{-37}{4}=-9.25\)

Answer:

\(K(-5.25,-9.25)\)