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

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

Detailed Solution:

Draw AB with midpoint:

(-8, -7) A _____________________________M(0, -4)___________________________ B (x, y) = (??. ??)

Given: M(x, y) = (0, -4), At A: (x₁ , y₁ ) = (-8, -7) At B: (x₂ , y₂) ) = (??. ??)

Midpoint Formula: M(x, y) = [ (x₁ + x₂)/2, (y₁ + y₂)/2 ] ==> (0, -4) = [ (-8 + x₂)/2, (-7 + y₂)/2 ] ==>

Therefore:

0 = (-8 + x₂)/2 ==> 0 = -8/2 + x₂/2 ==> x₂/2 = 4 ==> x₂ = 8

-4 = (-7 + y₂)/2 ==> -4 = -7/2 + y_2/2==> y_2/2 = -4 + 7/2==> y_2/2 = (-8 + 7)/2==> y_2/2 = -1/2==> y₂ = -1

At B: (x₂ , y₂) ) = (8. -1) (Final Answer)

Check: M(0, -4) (x₁ , y₁ ) = (-8, -7) (x₂ , y₂) ) = (8. -1)

M(x, y) = [ (x₁ + x₂)/2, (y₁ + y₂)/2 ] ==> (0, -4) = [ (-8 + 8)/2, (-7 + -1)/2 ] ==> (0, -4) = [ (0)/2, (-8)/2 ] ==>

(0, -4) = (0, -4)

Answer 2

One posting of a problem is sufficient.