# Math Help - Endpoint question

1. ## Endpoint question

GivenP(-7,2) is one endpoint of the line segment PQ and M(-5,6) is the midpoint of PQ, find the coordinates of the other endpoint Q.

2. If a and b are ordinate or abcissa of two points then mid point say c is given by
c=(a+b)/2
in your question,mid point is given.
So let us consider the abcissa first
-5=(-7+a)/2
a-7=-10
a=-3
hence the abcissa of the end point is -3.similarly you can find the ordinate of the end point.

3. Is the other coordinate 6?

4. Originally Posted by euclid2
GivenP(-7,2) is one endpoint of the line segment PQ and M(-5,6) is the midpoint of PQ, find the coordinates of the other endpoint Q.

Originally Posted by euclid2
Is the other coordinate 6?
No... Call the point Q = (a,b) and lets follow Nikhil's idea:

$\frac{(-7,2) + (a,b)}{2} = (-5,6)$

But now let us solve it together,

$(-7,2) + (a,b) = 2(-5,6) = (-10,12)$

$(-7,2) + (a,b) = (-7+a,2+b) = (-10,12)$

$(-7+a,2+b) = (-10,12) \Rightarrow -7+a = -10, 2+b = 12 \Rightarrow a=-3,b=10$

Thus Q(-3,10) is the other end point.

5. Ok thanks, thats where I got confused and divided instead of subtracted.
(-7+x)/2=-5
-7x=-10
x=-3
(2x+y)/2=6
2y=6*2
y=12-2-where i divided instead, my mistake
y=10

Thanks.