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.
Thanks alot in advance
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.
No... Call the point Q = (a,b) and lets follow Nikhil's idea:
$\displaystyle \frac{(-7,2) + (a,b)}{2} = (-5,6)$
But now let us solve it together,
$\displaystyle (-7,2) + (a,b) = 2(-5,6) = (-10,12)$
$\displaystyle (-7,2) + (a,b) = (-7+a,2+b) = (-10,12)$
$\displaystyle (-7+a,2+b) = (-10,12) \Rightarrow -7+a = -10, 2+b = 12 \Rightarrow a=-3,b=10$
Thus Q(-3,10) is the other end point.