If (3,5) is the midpoint of the line segment ST and the coordinates of S are (2,7) find coordinates of T

Work Shown:

Let T be the point (x,y)

Point S is defined to be at (2,7)

The x coordinates of S and T are 2 and x in that order. Add them up and divide by 2 to get (2+x)/2. Set this equal to 3 as this is the x coordinate of the midpoint. We have this equation

(2+x)/2 = 3

Now solve for x

(2+x)/2 = 3

2+x = 2*3 multiply both sides by 2

2+x = 6

x = 6-2 subtract 2 from both sides

x = 4

We'll follow similar logic and steps for the y coordinate of point T

S = (2,7)

T = (x,y)

The y coordinates for S and T are 7 and y in that order.

Add them up, divide by 2, then set the result equal to 5 (which is the y coordinate of the midpoint). Then solve for y.

(7+y)/2 = 5

7+y = 2*5 multiply both sides by 2

y+7 = 10

y = 10-7 subtract 7 from both sides

y = 3

Point T gets updated from (x,y) to (4, 3)

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