Answer :
R(–3, 4)
Step-by-step explanation:
Let Q(-9,8) and S(9,-4) be the given points and let R(x, y) divides QS in the ratio 1:2.
By section formula,
[tex]R(x, y)=R\left(\frac{m x_{2}+n x_{1}}{m+n}, \frac{m y_{2}+n y_{1}}{m+n}\right)[/tex]
Here, [tex]x_{1}=-9, y_{1}=8, \text { and } x_{2}=9, y_{2}=-4 \text { and } m=1, n=2[/tex]
Substituting this in the section formula
[tex]R(x, y)=R\left(\frac{1(9)+2(-9)}{1+2}, \frac{1(-4)+2(8)}{1+2}\right)[/tex]
To simplifying the expression, we get
[tex]\Rightarrow R(x, y)=R\left(\frac{9-18}{3}, \frac{-4+16}{3}\right)[/tex]
[tex]\Rightarrow R(x, y)=R\left(\frac{-9}{3}, \frac{12}{3}\right)[/tex]
⇒ R(x,y) = R(–3,4)
Hence, the coordinates of point R is (–3, 4).
The coordinate of point R is given by the section formula with ratio 1: 2 is (-3, 4).
What is coordinate geometry?
Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of line, etc.
The coordinates of the endpoint of QS are Q(-9,8) and S(9,-4). Point R is on cue as such that QR: RS Is in the ratio 1: 2.
Let the coordinate of the R be (x, y).
We know that the section formula is given as
[tex]\rm (x, y) = ( \dfrac{m_1x_2 + m_2x_1}{m_1 + m_2}, \dfrac{m_1y_2 + m_2y_1}{m_1 + m_2})\\\\(x, y) = ( \dfrac{1*9+2(-9)}{1+2}, \dfrac{1*(-4) + 2*8}{1+2})\\\\(x, y) = ( \dfrac{-9}{3}, \dfrac{12}{3})\\\\(x, y) = (-3,4)[/tex]
More about the coordinate geometry link is given below.
https://brainly.com/question/1601567