Question

On a coordinate grid. AB has endpoints A(4,– 2) and B(x, y). The midpoint of AB (-3,1). What is the x-coordinate of point B?

Answer 1

Answer: -10

Explanation:

Formula for mid point is :

Mid point = ( (x1+x2)÷2 , (y1+y2)÷2) )

So, X1 = 4

X2 = X

Y1 = -2

Y2 = y

Now, use the formula

(-3,1) = ( (4 + x)÷2 , (-2+y)÷2) )

Now divide the sides for yourself to solve for midpoint for X and y separately

-3 = (4+x) ÷ 2 and 1 = (-2+y) ÷ 2

This is because 3 is the x coordinate of the mid point of A and B , so we equate it to (4+x) ÷ 2 because this expression basically gives us the x coordinate of mid point of A and B. So we already have the x coordinate of midpoint which is -3 so we can use this to find X coordinate of point B

So then we solve it by multiplying the 2 with -3 which gives -6

-6 = 4+X

Shift 4 on the other side and it will become negative 4

-6-4 = X

X = -10