Question 160068
M is the midpoint of XY. X has coordinates (2, 7)and M has coordinates (6, 1). Find the coordinates of Y.

Let (x,y) be the coordinates of Y. Then, by the midpoint formula:

midpoint = [(x1 + x2)/2 , (y1 + y2)/2]

We are given the midpoint to be the point (6, 1).

Let midpoint = (6, 1)

(6, 1) = [(x + 2)/2 , (y + 7)/2]

Do you see the point (6,1)?

To find the coordinates of the y point, we equate (x + 2)/2 to 6

and then we equate (y + 7)/2 to 1 and solve for x and y individually.

(x + 2)/2 = 6

x + 2 = 6 * 2

x + 2 = 12

x = 12 - 2

x = 10

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(y + 7)/2 = 1

y + 7 = 1 * 2

y + 7 = 2

y = 2 - 7

y = -5

The coordinates of point y are x = 10 and y = -5 written (10, -5).

Did you follow?