Question

find the coordinates of point s on $overline{qr}$ such that the ratio of qs to sr is 1:3. q(2, 5) r(-2, -3)

Explanation:

Step1: Recall section - formula

The formula for finding the coordinates of a point \(S(x,y)\) that divides the line - segment joining \(Q(x_1,y_1)\) and \(R(x_2,y_2)\) in the ratio \(m:n\) is \(x=\frac{mx_2+nx_1}{m + n}\) and \(y=\frac{my_2+ny_1}{m + n}\). Here, \(x_1 = 2,y_1 = 5,x_2=-2,y_2=-3,m = 1,n = 3\).

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

Substitute the values into the \(x\) - formula: \(x=\frac{1\times(-2)+3\times2}{1 + 3}=\frac{-2 + 6}{4}=\frac{4}{4}=1\).

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

Substitute the values into the \(y\) - formula: \(y=\frac{1\times(-3)+3\times5}{1 + 3}=\frac{-3 + 15}{4}=\frac{12}{4}=3\).

Answer:

\((1,3)\)