Answer:
(-16,24)
Step-by-step explanation:
In this problem, we have segment PR, where the endpoins have coordinates
P (-22, 32)
R (5, -4)
We want to find point Q along the segment such that
PQ : QR = 2 : 7 (1)
We can write the coordinates of point Q as
[tex]Q(x_P,y_P)[/tex]
So we can now rewrite eq(1) for both the x- and y- variable:
[tex]\frac{x_Q-x_P}{x_R-x_Q}=\frac{2}{7}[/tex] (2)
[tex]\frac{y_Q-y_P}{y_R-y_Q}=\frac{2}{7}[/tex] (3)
We start by solving eq(2) to find the coordinate x of point Q:
[tex]7(x_Q-x_P) = 2(x_R-x_Q)\\7x_Q-7x_P=2x_R-2x_Q\\9x_Q=2x_R+7x_P\\x_Q=\frac{2x_R+7x_P}{9}=\frac{2(5)+7(-22)}{9}=-16[/tex]
While for the y-coordinate:
[tex]7(y_Q-y_P) = 2(y_R-y_Q)\\7y_Q-7y_P=2y_R-2y_Q\\9y_Q=2y_R+7y_P\\y_Q=\frac{2y_R+7y_P}{9}=\frac{2(-4)+7(32)}{9}=24[/tex]
So the coordinates of Q are (-16,24).
The coordinate of Q is [tex]Q=(-16,4)[/tex]
To understand more, check below explanation.
To find the coordinate of Q, we use section formula,
[tex]Q=(\frac{m_{1}x_{2}+m_{2}x_{1}}{m_{1}+m_{2}},\frac{m_{1}y_{2}+m_{2}y_{1}}{m_{1}+m_{2}} )[/tex]
It is given that,
[tex](x_{1},y_{1})=(-22,32),(x_{2},y_{2})=(5,-4), m_{1}=2,m_{2}=7[/tex]
Substitute above values in above section formula,
[tex]Q=(\frac{(2*5)+(7*-22)}{2+7}, \frac{(2*32)+(7*-4)}{2+7})\\\\Q=(-\frac{144}{9} ,\frac{36}{9} )\\\\Q=(-16,4)[/tex]
Therefore, the coordinate of Q is [tex]Q=(-16,4)[/tex]
Learn more about the section formula here:
https://brainly.com/question/26433769
