Answer:
The coordinates of R are [tex](x_1,y_1)=(4,5)[/tex]
Step-by-step explanation:
Given : M(5, 7) is the midpoint of RS. The coordinates of S are (6, 9).
To find : What are the coordinates of R?
Solution :
We have given,
A line RS which has a mid point M.
Let, the coordinates of R be [tex](x_1,y_1)[/tex]
The coordinates of S are [tex](x_2,y_2)=(6, 9)[/tex]
The coordinates of M are [tex](x_3,y_3)=(5,7)[/tex]
Applying mid-point formula,
[tex](x_3,y_3)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
[tex](5,7)=(\frac{x_1+6}{2},\frac{y_1+9}{2})[/tex]
Solve separately,
x- coordinate is
[tex]\frac{x_1+6}{2}=5[/tex]
[tex]x_1+6=10[/tex]
[tex]x_1=4[/tex]
y- coordinate is
[tex]\frac{y_1+9}{2}=7[/tex]
[tex]y_1+9=14[/tex]
[tex]y_1=5[/tex]
So, The coordinates of R are [tex](x_1,y_1)=(4,5)[/tex]
