Practice: Points and Lines in the Plane

Question

The midpoint of AB is at (4,1). If A=(1,4), find B.

Answer 1

Could also do it as follows:

The x change from Pt. A to the midpoint is +3 (4 - 1)

The y change from Pt. A to the midpoint is -3 (1 - 4)

To find Pt. B, apply the same changes from midpoint (4,1)

So x becomes 4 + 3 = 7

y becomes 1 - 3 = -2

Helps to draw a picture, especially if you have some graph paper.

Answer 2

Let B = (x, y)

Then, (x+1) / 2 = 4 and (y + 4) / 2 = 1

Solve for x and y.