SOLUTION: Find the coordinates of Q given the M is the midpoint of PQ. P(6,-2),M(0,5),Q(?,?) Thanks for your help.

Algebra ->  Coordinate-system -> SOLUTION: Find the coordinates of Q given the M is the midpoint of PQ. P(6,-2),M(0,5),Q(?,?) Thanks for your help.      Log On


   



Question 924137: Find the coordinates of Q given the M is the midpoint of PQ. P(6,-2),M(0,5),Q(?,?) Thanks for your help.
Found 2 solutions by ewatrrr, MathLover1:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
P(6, -2)
Q(x, y) M(0,5): ( %286+%2B+x%29%2F2, +%28-2+%2B+y%29%2F2++%29)
Q(-6, 12)

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
P(6,-2),M(0,5),Q(x2,y2)

Since formula for midpoint is:
%28x1+%2B+x2%29+%2F+2 and %28y1+%2B+y2%29+%2F+2
Then formula for x2 and y2 is:
x2+=+2%28Mx%29+-+x1
y2+=+2%28My%29+-+y1
where Mx is the x coordinate of the midpoint, and My the y coordinate of the midpoint
so, we have:
x2+=+2%28Mx%29+-+x1
x2+=+2%280%29+-+6
x2+=+0+-+6
x2+=+-6
y2+=+2%28My%29+-+y1
y2+=+2%285%29+-+%28-2%29
y2+=+10+%2B2
y2+=12
so, Q(x2,y2)=Q(-6,12)
Checking:
M+=+%28x1+%2B+x2%29+%2F+2 and %28y1+%2B+y2%29+%2F+2
M+=+%286+%2B%28-6%29%29+%2F+2 and %28-2+%2B+12%29+%2F+2
M+=+%286-6%29+%2F+2 and %28-2+%2B+12%29+%2F+2
M+=+0%2F+2 and 10+%2F+2
M = 0, 5
We got the right midpoint.
Thus, the coordinates of Q are (-6,+12)