Question

What is the length of AB if A and B have coordinates of A (-3,7) and B (7,3)​

Answer 1

AB = √116 ≈ 10.77

Explanation:

Use the formula that calculate the distance between two points:

`L = \sqrt{(x_(2) - x_(1))^(2)+(y_(2) - y_(1))^(2)}`

L means length

For the x and y, substitute a coordinate value that you will label as set 1 or 2.

For example:

A (-3, 7) will be set 1. x₁ = -3 y₁ = 7

B (7 , 3) will be set 2. x₂ = 7 y₂ = 3

Substitute the points into the formula to find the length AB. Simplify.

`L = \sqrt{(x_(2) - x_(1))^(2)+(y_(2) - y_(1))^(2)}`

`AB = \sqrt{(7 - (-3))^(2)+(3 - 7)^(2)}` Solve inside the brackets first

`AB = \sqrt{(10)^(2)+(-4)^(2)}` Square each term under the root

`AB = √(100+16)` Add under the root

`AB = √(116)` Final exact answer is radical (root) form

`AB = 10.77` Final approximate or rounded answer to 2 decimals

The length of AB is the squareroot of 116, or about 10.77 units.