Question

point e lies on \\( \overline { c d } \\) such that \\( c e : d e \\) is \\( 2 : 1 \\). graph e.

Explanation:

Step1: Find coordinates of C and D

From the graph, \(C(-6,9)\) and \(D(-3,-3)\)

Step2: Use the section formula

If a point \(E(x,y)\) divides the line - segment joining \(C(x_1,y_1)\) and \(D(x_2,y_2)\) in the ratio \(m:n\), then \(x=\frac{mx_2 + nx_1}{m + n}\) and \(y=\frac{my_2+ny_1}{m + n}\). Here \(m = 2\), \(n = 1\), \(x_1=-6\), \(y_1 = 9\), \(x_2=-3\), \(y_2=-3\)

Calculate \(x\) - coordinate of \(E\)

\(x=\frac{2\times(-3)+1\times(-6)}{2 + 1}=\frac{-6-6}{3}=\frac{-12}{3}=-4\)

Calculate \(y\) - coordinate of \(E\)

\(y=\frac{2\times(-3)+1\times9}{2 + 1}=\frac{-6 + 9}{3}=\frac{3}{3}=1\)

Answer:

The coordinates of point \(E\) are \((-4,1)\)