Question

M(1, 7) is the midpoint of PQ¯¯¯¯¯ . The coordinates of point P are (−8, 3) .

What are the coordinates of point Q?

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Answer 1

The midpoint is given as (1,7)
We are given one endpoint (-8,3) which can represent (x1,y1).
We need to get the other endpoint represented by (x2,y2)

1- The x-coordinate:
The x-coordinate of the midpoint is calculated using the following rule:
Xmidpoint = (x1+x2) / 2
1 = (-8+x2) / 2
2 = -8 + x2
x2 = 2+8
x2 = 10
The x-coordinate of Q is 10

2- The y-coordinate:
The y-coordinate of the midpoint is calculated using the following rule:
Ymidpoint = (y1+y2) / 2
7 = (3+y2) / 2
14 = 3+y2
y2 = 14-3
y2 = 11
The y-coordinate of Q is 11

Based on the above calculations, the coordinates of point Q are (10,11)

Answer 2

(10, 11)  
Since M is the midpoint of PQ, that means that the distance between P and M is the same as the distance between M and Q. So the answer will be 
(M-P)+M  
Let's substitute the known values and do the math: 
(M-P)+M 
= M - P + M
 = (1,7) - (-8,3) + (1,7)
 = (1 - -8 + 1, 7 - 3 + 7)
 = (10, 11) 
 So the location of point Q is (10, 11). 
 Let's verify that answer. If we calculate the average of P and Q, we should
get M. So
 ((-8 + 10)/2, (3+11)/2)
 = (2/2, 14/2)
 = (1, 7) 
 And we get the correct value for M, so our answer is correct.