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

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)= ( , )

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 )

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.

To find the other point (x2, y2), we can use the formula for the midpoint of two points.

Given that the midpoint is (6,2) and one of the points is (3,5), we can substitute these values into the formula:

x_m = (x_1 + x_2)/2

6 = (3 + x_2) / 2

To solve for x2, we can multiply both sides of the equation by 2 to remove the denominator:

12 = 3 + x_2

Subtract 3 from both sides of the equation to isolate x2:

x_2 = 12 - 3

x_2 = 9

Now let's find the value of y2:

y_m = (y_1 + y_2)/2

2 = (5 + y_2) / 2

To solve for y2, we can multiply both sides of the equation by 2 to remove the denominator:

4 = 5 + y_2

Subtract 5 from both sides of the equation to isolate y2:

y_2 = 4 - 5

y_2 = -1

Therefore, the other point is (9, -1).

Endpoint (x2, y2) = (9, -1)