Question

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

Answer 1

Answer:

AB = √116 ≈ 10.77

Step-by-step 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

$AB = \sqrt{100+16}$    Add under the root

$AB = \sqrt{116}$     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.