Question

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

Answer 1

Answer:-10

Step-by-step 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

Answer 2

Answer:

B (-10,4)

Step-by-step explanation:

Given A (4,-2) and midpoint M (-3,1) we can find equation of the line

y = mx +b

slope m = raise / run

m = (y1 - y2) / (x1 - x2)

m = (-2 - 1) / (4 - -3)

m = -3 / 7 = -3/7

given the midpoint M, then point B (x,y) must have the same length and slope as AM. So point B must have twice the rise and twice the run.

Slope was -3/7 so segment AB must be 2(slope) = -6/14, so from point A, point B will be from A (4,-2)

raise = y1 - y2 = -6

-2 - y2 = -6

-y2 = -6 + 2

y2 = 4

run = x1 - x2 = 14 = 4 - x2

14 - 4 = -x2

x2 = -10