The midpoint of AB is M (-2,-2). If the coordinates of A are (-3,-6), what are the coordinates of B?

Answer 1

Hi Janet,

Apply the midpoint formula, but do it essentially in reverse. Midpoint is known, so:

(-2, -2) = (x1 + x2)/2, (y1+y2/2)

x1, y1 are coordinates of point a; x2, y2 are coordinates of point b.

Let's start with the x-coordinate--you know the midpoint and the x-coordinate of point a, so solve for x2:

-2 = (-3 + x2)/2

-4 = -3 +x2

x2= -1

Now, for the y-coordinate--you know the midpoint and the y-coordinate of point a:

-2 = (-6 + y2)/2

-4 = -6 +y2

y2=2

Point b coordinates are (-1,2).

I hope this helps.

Answer 2

Soving such problems is somewhat easier after developing a formula for finding the unknown endpoint given the midpoint and the the other endpoint.

With a small amount of Algebra, we find that all we need to do is double the x midpoint value and then subtract the given x endpoint. Next we do the same for the given y-values.

Let's do the x-values first:

2 * ( -2 ) - ( -3 ) = ( -4 ) + 3 = -1

We can easily check this by using the standard midpoint formmula:

[ ( -3) + ( -1 ) ] / 2 = ( -4 ) / 2 = -2

Now let's find the unknown y endpoint:

2 * ( -2 ) - ( - 6 ) = ( -4 ) + 6 = 2

Now let's verify by using the standard midpoint formula:

[ ( -6 ) + ( 2 ) ] / 2 = ( - 4 ) / 2 = -2

It makes no sense to keep solving the same equation over and over when it can be done once to determine a generic formula and save time:

x₂ = 2 * x_m - x₁

y₂ = 2 * y_m - y₁

This is easy to remember:

Double the given x endpoint, and then subtract the given x endpoint.

Then do the same for the y values.

There is no need to reinvent the wheel!

Answer 3