The midpoint of AB is M(0, -4). If the coordinates of A are (-8, -7), what are the coordinates of B?

Question

this is my geometry classwork, need help asap

Answer 1

(x_m, y_m) = coordinates of the midpoint

Formulas

x_m = (x_A + x_B)/2

y_m = (y_A + y_B)/2

Data we do have:

We know that the midpoint of AB is M(0, -4) --> x_m=0 and y_m=-4

We know that the coordinates of A are (-8, -7) --> x_A=-8 and y_A=-7

We are looking for the coordinates of B (x_B, y_B) --> x_B=? and y_B=?

We can start by finding the X_B by substituting the value in the formula we have:

Frist, for x_m

x_m = (x_A + x_B)/2 <--> Remember that x_m=0 x_A=-8 x_B=?

Substituting the values (plug the values in)

0 = (-8 + x_B)/2 --> We multiply both sides of the equation by 2

0 *2 = (-8 + x_B)/2 *2 We simplify

0 = (-8 + x_B)/2 *2

0 = -8 + x_B We add 8 on both sides

0 +8 = -8 + x_B +8 We cancel the "zero pairs" (8 and -8) on the right of the equal sign

0 +8 = -8 + x_B +8

8 = x_B We can rewrite it as

x_B = 8

We can do the same for calculating y_B

y_m = (y_A + y_B)/2 <--> Remember that y_m=-4 y_A=-7 y_B=?

Substituting the values (plug the values in)

-4 = (-7 + y_B)/2 We multiply by 2 both sides of the equation

-4 *2 = (-7 + y_B)/2 *2 O the left side (-4*2 = -8). On the right side we simplify (cancel out).

-8 = -7 + y_B We add 7 on both sides

-8 +7 = -7 + y_B +7 on the left side (-8 +7 --> -1). On the right side we cancel the "zero pairs" (-7 and +7)

-1 = -7 + y_B +7

-1 = y_B We can rewrite it as

y_B = -1

We already found x_B = 8 and y_B = -1

Therefore the coordinates of the B point are

B (x_B, y_B) --> Substituting the values: x_B = 8 and y_B = -1

B (8, -1) This is the final answer

Answer 2

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