Question

Find the coordinates of the missing endpoint if P is the midpoint of Line Segment NQ.

19. N( 2, 0), P( 5, 2)

20. N( 5, 4), P( 6, 3)

21. Q( 3, 9), P( -1, 5)

(I need the explanation on how to solve problems like these; just the answer wont help)

Answer 1

• Midpoint formula is $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$ .

19.

So starting with this one, we will be solving for the coordinates of the unknown endpoint separately. Starting with the x-coordinate, since we know that the midpoint x-coordinate is 5 and the x-coordinate of N is 2, our equation is set up as such: $\frac{x+2}{2}=5$ From here we can solve for the x-coordinate of Q.

Firstly, multiply both sides by 2: $x+2=10$

Next, subtract both sides by 2 and your x-coordinate is $x=8$

With finding the y-coordinate, it's a similar process as with the x-coordinate except that we are using the y-coordinates of the midpoint and endpoint N.

$\frac{y+0}{2}=2\\ y=4$

Putting it together, the missing endpoint is (8,4).

(The process is pretty much the same with the other problems, so I'll go through them real quickly.)

20.

$\frac{x+5}{2}=6\\ x+5=12\\ x=7$

$\frac{y+4}{2}=3\\ y+4=6\\ y=2$

The missing endpoint is (7,2).

21.

$\frac{x+3}{2}=-1\\ x+3=-2\\ x=-5$

$\frac{y+9}{2}=5\\ y+9=10\\y=1$

The missing endpoint is (-5,1).