Answer:
The coordinates of point R are (6 , 3)
Step-by-step explanation:
* Lets revise the rule of the mid-point
- The mid point (x , y)of a line whose end points are [tex](x_{1},y_{1})[/tex]
and [tex](x_{2},y_{2})[/tex] is [tex](\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})[/tex]
∵ M is the mid point of line RS
∵ The coordinates of point M are (7 , 5)
∴ x = 7 and y = 5
∵ The coordinates of point R are [tex](x_{1},y_{1})[/tex]
∵ The coordinates of point S are (8 , 7)
∴ [tex](x_{2},y_{2})[/tex] = (8 , 7)
∴ [tex]x_{2}=8[/tex] and [tex]y_{2}=7[/tex]
- By using the rule above
∵ [tex]x=\frac{x_{1}+x_{2}}{2}[/tex]
∵ [tex]7=\frac{x_{1}+8}{2}[/tex]
- Multiply both sides by 2
∴ [tex]14=x_{1}+8[/tex]
- Subtract both sides by 8
∴ [tex]x_{1}=6[/tex]
∴ the x-coordinate of point R is 6
∵ [tex]y=\frac{y_{1}+y_{2}}{2}[/tex]
∵ [tex]5=\frac{y_{1}+7}{2}[/tex]
- Multiply both sides by 2
∴ [tex]10=y_{1}+7[/tex]
- Subtract both sides by 7
∴ [tex]y_{1}=3[/tex]
∴ the y-coordinate of point R is 3
* The coordinates of point R are (6 , 3)
