Question

1. find point z on $overline{rs}$ with r (-1, 1) and s (7, 2) such that the ratio of rz to zs is 1:3.

Explanation:

Step1: Recall the section - formula

The formula to find the coordinates of a point \(Z(x,y)\) that divides the line - segment joining \(R(x_1,y_1)\) 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, \(x_1=-1,y_1 = 1,x_2 = 7,y_2 = 2,m = 1,n = 3\).

Step2: Calculate the x - coordinate of point Z

\[x=\frac{1\times7+3\times(-1)}{1 + 3}=\frac{7-3}{4}=\frac{4}{4}=1\]

Step3: Calculate the y - coordinate of point Z

\[y=\frac{1\times2+3\times1}{1 + 3}=\frac{2 + 3}{4}=\frac{5}{4}=1.25\]

Answer:

The coordinates of point \(Z\) are \((1,1.25)\)