Question

the point k lies on the segment jl. find the coordinates of k so that the ratio of jk to kl is 7 to 2. l (24, 32) k (?,?) j (-3, -4) 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, \(x_1=-3,y_1=-4,x_2 = 24,y_2 = 32,m = 7,n = 2\).

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

\[

$$\begin{align*} x&=\frac{7\times24+2\times(-3)}{7 + 2}\\ &=\frac{168-6}{9}\\ &=\frac{162}{9}\\ &=18 \end{align*}$$

\]

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

\[

$$\begin{align*} y&=\frac{7\times32+2\times(-4)}{7 + 2}\\ &=\frac{224 - 8}{9}\\ &=\frac{216}{9}\\ &=24 \end{align*}$$

\]

Answer:

\((18,24)\)