Question

rs has endpoints r(-11, 10) and s(-6, -5). point t divides rs such that st:tr is 2:3. what are the coordinates of t? write your answers as integers or decimals.

Explanation:

Step1: Recall the section - formula

If a point \(T(x,y)\) divides the line - segment joining \(R(x_1,y_1)\) and \(S(x_2,y_2)\) in the ratio \(m:n\), then \(x=\frac{mx_1+nx_2}{m + n}\) and \(y=\frac{my_1+ny_2}{m + n}\). Here, \(R(-11,10)\), \(S(-6,-5)\), and the ratio \(m:n = 2:3\).

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

\(x=\frac{2\times(-11)+3\times(-6)}{2 + 3}=\frac{-22-18}{5}=\frac{-40}{5}=-8\)

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

\(y=\frac{2\times10+3\times(-5)}{2 + 3}=\frac{20 - 15}{5}=\frac{5}{5}=1\)

Answer:

\((-8,1)\)