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

Explanation:

Hey there!!

It's so simple.

While finding the coordinates of any point if the midpoint is there it will be much easier. You must remember the midpoint formulae.

Let's simply work with it.

Here, A (2,-1) and midpoint M(3,3) are given.

Let another coordinate be B(x,y).

By midpoint formulae,

`midpoint(x.y) = (x1 + x2)/(2) ,(y1 + y2)/(2)`

Putting their values,

`m(3 , 3) = (2 + x)/(2) , ( - 1 + y)/(2)`

As they are equal, equating with their corresponding elements we get,

`3 = (2 + x)/(2)`

6= 2 + x

x = 6-2

Therefore, the value of a is 4.

Again,

`3 = ( - 1 + y)/(2)`

6 = -1 + y

Therefore, the value of y is 7.

Therefore, the coordinates are B (4,7)

Hope it helps....