Question

Pretest: Coordinate Geometry4Line segment PQ is a directed line segment beginning at P(6,-5) and ending at Q(-2,4).Find point R on The line segment PQ that partition it into the segments PR and RQ in the ratio 3:2

Answer 1

Given:

The point is that P and Q

$\begin{gathered} P(6,-5) \\ \\ Q(-2,4) \end{gathered}$

The point of ratio is:

$m:n=3:2$

Find-:

The point of "R"

Explanation-:

If the line ratio is m:n is:

$\begin{gathered} A=(x_1,y_1) \\ \\ B=(x_2,y_2) \end{gathered}$

Point "C" is:

$C=(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})$

The given point and ratio is:

$\begin{gathered} m:n=3:2 \\ \\ P=(x_1,y_1)=(6,-5) \\ \\ Q=(x_2,y_2)=(-2,4) \end{gathered}$$R=(\frac{3(-2)+2(6)}{3+2},\frac{3(4)+2(-5)}{3+2})$

The point so,

$\begin{gathered} R=(\frac{-6+12}{5},\frac{12-10}{5}) \\ \\ \\ R=(\frac{6}{5},\frac{2}{5}) \\ \\ \end{gathered}$

The point of R is (6/5, 2/5)