Question

M(7, 5) is the midpoint of line RS The coordinates of S are (8, 7). What are the coordinates of R?

Answer 1

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 $(x_{1},y_{1})$

 and $(x_{2},y_{2})$ is $(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$

∵ 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 $(x_{1},y_{1})$

∵ The coordinates of point S are (8 , 7)

∴ $(x_{2},y_{2})$  = (8 , 7)

∴ $x_{2}=8$ and $y_{2}=7$

- By using the rule above

∵ $x=\frac{x_{1}+x_{2}}{2}$

∵ $7=\frac{x_{1}+8}{2}$

- Multiply both sides by 2

∴ $14=x_{1}+8$

- Subtract both sides by 8

∴ $x_{1}=6$

∴ the x-coordinate of point R is 6

∵ $y=\frac{y_{1}+y_{2}}{2}$

∵ $5=\frac{y_{1}+7}{2}$

- Multiply both sides by 2

∴ $10=y_{1}+7$

- Subtract both sides by 7

∴ $y_{1}=3$

∴ the y-coordinate of point R is 3

* The coordinates of point R are (6 , 3)