Question

The midpoint of AB is M(3,-3). If the coordinates of A are (2, -1), what are the

coordinates of B?

Answer 1

The coordinates of B is (4, 7)

Explanation:

To find the answer for B, you have to do the inverse of the midpoint formula, which is M equals (x1 multiplied by x2, over 2; y1 multiplied by y2, over 2).

If you substitute in A's coordinates for x1 and y1, you come up with (3, 3) = (2+x, over 2; and -1+y, over 2)

If the x coordinate answer for AB was 3, you can create an equation like this to solve for B's x coordinate: 2+x over 2 equals 3.

you multiply 2 by 3 to get 6---> 2+x=6-----> x=4

If the y coordinate for AB was also three, you can create another equation to solve for B's y coordinate: -1+y over 2 equals 3.

you multiply 2 by 3 to get 6 again---->so -1+y=6---->y=7

so the answer for B's coordinates is (4, 7).

Answer 2

• B(4, - 5)

--------------------------

Given:

• A = (2, - 1),
• Midpoint M = (3, - 3),

Find the coordinates of the other end point B.

Use midpoint equation, considering point B as (x, y):

• 3 = (2 + x)/2 ⇒ 2 + x = 2*3 ⇒ 2 + x = 6 ⇒ x = 4,
• - 3 = (- 1 + y)/2 ⇒ -1 + y = 2*(-3) ⇒ -1 + y = - 6 ⇒ y = - 5.

Therefore the point B has coordinates of (4, - 5).