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=((mx_2+nx_1)/(m+n),(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=((3(-2)+2(6))/(3+2),(3(4)+2(-5))/(3+2))`

The point so,

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

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