The midpoint of two points is (6,2). If one of the points is (3,5), find the other point.

Question

x_m = (x_1 + x_2)/2

6 = (3 + x_2) / 2

= 3 + x_2

x_2 =

y_m = (y_1 + y_2)/2

2 = (5 + y_2) / 2

= 5 + y_2

y_2 =

Endpoint (x_2, y_2)= ( , )

Answer 1

xm = 6

ym = 2

x1 = 3

y1 = 5

xm = ( x1 + x2 ) / 2

6 = ( 3 + x2 ) / 2 Multiply both sides by 2

6 * 2 = 2 * ( 3 + x2 ) / 2

12 = 3 + x2 Subtract 3 to both sides

12 - 3 = 3 + x2 - 3

9 = x2

x2 = 9

ym = ( y1 + y2 ) / 2

2 = ( 5 + y2 ) / 2 Multiply both sides by 2

2 * 2 = 2 * ( 5 + y2 ) / 2

4 = 5 + y2 Subtract 5 to both sides

4 - 5 = 5 + y2 -5

- 1 = y2

y2 = - 1

The other point:

( 9 , - 1 )

Answer 2

The midpoint of two points is (6,2). One of the points is (3,5).

Since the two ends must be equidistant from the midpoint,

3 = 6-3, 9 = 6+3
5 = 2+3, -1 = 2-3
So, (9,-1) is at the other end.