Question

the point k lies on the segment jl. find the coordinates of k so that the ratio of jk to kl is 2 to 5. j(-7,2) k(?,?) l(28, - 12)

Explanation:

Step1: Recall 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, \(m = 2\), \(n = 5\), \(x_1=-7\), \(y_1 = 2\), \(x_2=28\), and \(y_2=-12\).

Step2: Calculate the x - coordinate of K

\[

$$\begin{align*} x&=\frac{2\times28 + 5\times(-7)}{2 + 5}\\ &=\frac{56-35}{7}\\ &=\frac{21}{7}\\ &=3 \end{align*}$$

\]

Step3: Calculate the y - coordinate of K

\[

$$\begin{align*} y&=\frac{2\times(-12)+5\times2}{2 + 5}\\ &=\frac{-24 + 10}{7}\\ &=\frac{-14}{7}\\ &=-2 \end{align*}$$

\]

Answer:

The coordinates of \(K\) are \((3,-2)\)