Question

midpoint (-19,-18) endpoint (-14,-19)

Answer 1

Answer:

Co-ordinates of endpoint is  (-24,-17)

Step-by-step explanation:

The question should be given as :

Find the coordinates of the other endpoint of the segment, given its midpoint (-19,-18) and one endpoint (-14,-19).

Step-by-step explanation:

Given point:

Endpoint (-14,-19)

Mid-point of segment  (-19,-18)

Let endpoint 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.

$M=(\frac{-14+x_2}{2},\frac{-19+y_2}{2})$

We know $M(-19,-18)$

So, we have

$(-19,-18)=(\frac{-14+x_2}{2},\frac{-19+y_2}{2})$

Solving for $x_2$  

$\frac{-14+x_2}{2}=-19$

Multiplying both sides by 2.

$\frac{-14+x_2}{2}\times 2=-19\times 2$

$-14+x_2=-38$

Adding both sides by 14.

$-14+x_2+14=-38+14$

∴ $x_2=-24$

Solving for $y_2$  

$\frac{-19+y_2}{2}=-18$

Multiplying both sides by 2.

$\frac{-19+y_2}{2}\times 2=-18\times 2$

$-19+y_2=-36$

Adding both sides by 19.

$-19+y_2+19=-36+19$

∴ $y_2=-17$

Thus co-ordinates of point N is (-24,-17)