Question

what are the coordinates of r on q s such that the ratio of q r to r s is 2:3? o (-8,6) o (-1.6,1.2) o -4 3,1 o (0.6,2.8)

Explanation:

Step1: Find coordinates of Q and S

From the graph, Q = (-6,-2) and S=(4,6).

Step2: Use section - formula

The section - formula for a point R(x,y) that divides the line - segment joining \(Q(x_1,y_1)\) and \(S(x_2,y_2)\) in the ratio \(m:n\) is \(x=\frac{mx_2+nx_1}{m + n}\) and \(y=\frac{my_2+ny_1}{m + n}\). Here, \(m = 2\) and \(n = 3\), \(x_1=-6\), \(y_1=-2\), \(x_2 = 4\), \(y_2=6\).
For x - coordinate of R:
\[

$$\begin{align*} x&=\frac{2\times4+3\times(-6)}{2 + 3}\\ &=\frac{8-18}{5}\\ &=\frac{-10}{5}\\ &=-2 \end{align*}$$

\]
For y - coordinate of R:
\[

$$\begin{align*} y&=\frac{2\times6+3\times(-2)}{2 + 3}\\ &=\frac{12 - 6}{5}\\ &=\frac{6}{5}\\ & = 1.2 \end{align*}$$

\]

Answer:

(-1.6,1.2)