Question

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


What are the coordinates of point Q?

Enter your answer in the boxes. ( , )

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

The coordinates of point P (x1,x2) = (â’8, 3). 
The coordinates of point Q (x2,y2)  
Midpoint of P and Q is M (xm, ym) = (1,7) 
xm = (x1 + x2)/2; ym = (y1 + y2)/2 
=> 1 = (-8 + x2)/2 => x2 - 8 = 2 => x2 = 10 
=> 7 = (3 + y2)/2 => y2 + 3 = 14 => y2 = 11 
Hence Q (x2, y2) = (10, 11).