Answer:
The coordinates of R are \((x_1,y_1)=(4,5)\)
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 \((x_1,y_1)\)
The coordinates of S are \((x_2,y_2)=(6, 9)\)
The coordinates of M are \((x_3,y_3)=(5,7)\)
Applying mid-point formula,
\((x_3,y_3)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\)
\((5,7)=(\frac{x_1+6}{2},\frac{y_1+9}{2})\)
Solve separately,
x- coordinate is
\(\frac{x_1+6}{2}=5\)
\(x_1+6=10\)
\(x_1=4\)
y- coordinate is
\(\frac{y_1+9}{2}=7\)
\(y_1+9=14\)
\(y_1=5\)
So, The coordinates of R are \((x_1,y_1)=(4,5)\)
