Find Endpoint from Midpoint and Endpoint

Question

the midpoint of AB is M (0,-3) if the coordinates of A are (6,-5) what are the coordinates of B

Answer 1

Coordinates of A are (6,-5) and let’s assume coordinates of B are (x,y)

Midpoint of AB is M(0,-3).

Use midpoint formula and solve both equations:

1.). (6+x)/2=0 2.) (-5+y)/2 = -3

(6+x)=0 Multiply 2 both sides -5+y = -6

x=-6. Subtract 6 both sides y = -1

Answer : coordinates of B are ( -6,-1)

Answer 2

Find Endpoint from Midpoint and Start-point. the midpoint of AB is M (0, –3) if the coordinates of A are (6, –5) what are the coordinates of B = (??, ??)

Detailed Solution:

Start-point: A = (x₁, y₁) = (6, –5) Midpoint: M = (x, y) = (0, –3) Endpoint: B = (x₂, y₂) = (??, ??)

A====================================M====================================B

Midpoint Formula: Midpoint: M = (x, y) = ( (x₁ + x₂)/2, (y₁ + y₂)/2)

Midpoint: M = (0, –3) = ( (x₁ + x₂)/2, (y₁ + y₂)/2)

Midpoint: M = (0, –3) = ( (6 + x₂)/2, (–5 + y₂)/2)

Therefore:

0 = (6 + x₂)/2 ==> 6 + x₂ = 0 ==> x₂ = –6

–3 = (–5 + y₂)/2 ==> –5 + y₂ = (2)(–3) ==> –5 + y₂ = –6 ==> y₂ = –6 + 5 ==> y₂ = –1

Endpoint: B = (x₂, y₂) = (–6, –1)

Check: M = (x, y) = ( (x₁ + x₂)/2, (y₁ + y₂)/2) ==> (0, –3) = ( (6 – 6)/2, (–5 – 1)/2) ==> (0, –3) = (0, –3)