Question

Segment AB has coordinates A (-6, 13) and B (10, -7). Find the distance from A to B and the midpoint of AB.

Answer 1

Distance: 4√41

Midpoint: (2, 3)

Explanation:

A: (-6, 13) B: (10, -7)

(x₁, y₁) (x₂, y₂)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(10 - (-6))² + (-7 - 13)²

d = √(16)² + (-20)²

d = √256 + 400

d = √656

d = √16 × 41

d = 4√41

midpoint:

(x₁ + x₂) (y₁ + y₂)

---------- , ------------

2 2

(-6 + 10) (13 + (-7))

---------- , ------------

2 2

4 6

---------- , ------------

2 2

Midpoint = (2, 3)

I hope this helps!