Question

4. M(7, 3) is the midpoint of RS. The coordinates of point S are (8,4). What are the

Answer 1

The co-ordinates of point R is (6 , 2)

Solution:

Given that M(7, 3) is the midpoint of RS

Also co-ordinates of point S is (8, 4)

To find: co-ordinates of point R

The midpoint of two points $P(x_1, y_1)$ and $Q(x_2, y_2)$ is given as:

$M=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)$

Here midpoint M = (7, 3) and point S $(x_1 , y_1) = (8, 4)$

Point R = $(x_2, y_2)$

Substituting the values in formula we get,

$(7,3)=\left(\frac{8+x_{2}}{2}, \frac{4+y_{2}}{2}\right)$

Comparing both the sides we get,

$\frac{8+x_{2}}{2}=7$ and $\frac{4+y_{2}}{2}=3$

On solving,

$\begin{array}{l}{14=8+x_{2}} \\\\ {x_{2}=6}\end{array}$

Also,

$\begin{array}{l}{4+y_{2}=6} \\\\ {y_{2}=2}\end{array}$

Thus the co-ordinates of point R is (6 , 2)