Question

The coordinates of point S are (8.4). What are the

Answer 1

Answer:

Co-ordinates of point R is (26,2)

Step-by-step explanation:

Given point:

Endpoint S(8,4)

Mid-point M of segment RS (17,3)

Let endpoint $R$ have co-ordinates $(x_2,y_2)$

Using midpoint formula:

$M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Where $(x_1,y_1)$ and $(x_2,y_2)$ are co-ordinates of the endpoint of the segment.

Plugging in values to find the midpoint of segment KN.

$M=(\frac{8+x_2}{2},\frac{4+y_2}{2})$

We know $M(17,3)$

So, we have

$(17,3)=(\frac{8+x_2}{2},\frac{4+y_2}{2})$

Solving for $x_2$  

$\frac{8+x_2}{2}=17$

Multiplying both sides by 2.

$\frac{8+x_2}{2}\times 2=17\times 2$

$8+x_2=34$

Subtracting both sides by 8.

$8+x_2-8=34-8$

∴ $x_2=26$

Solving for $y_2$  

$\frac{4+y_2}{2}=3$

Multiplying both sides by 2.

$\frac{4+y_2}{2}\times 2=3\times 2$

$4+y_2=6$

Subtracting both sides by 4.

$4+y_2-4=6-4$

∴ $y_2=2$

Thus co-ordinates of point R is (26,2)  (Answer)