Answer:
AB = √116 ≈ 10.77
Step-by-step explanation:
Use the formula that calculate the distance between two points:
[tex]L = \sqrt{(x_{2} - x_{1})^{2}+(y_{2} - y_{1})^{2}}[/tex]
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.
[tex]L = \sqrt{(x_{2} - x_{1})^{2}+(y_{2} - y_{1})^{2}}[/tex]
[tex]AB = \sqrt{(7 - (-3))^{2}+(3 - 7)^{2}}[/tex] Solve inside the brackets first
[tex]AB = \sqrt{(10)^{2}+(-4)^{2}}[/tex] Square each term under the root
[tex]AB = \sqrt{100+16}[/tex] Add under the root
[tex]AB = \sqrt{116}[/tex] Final exact answer is radical (root) form
[tex]AB = 10.77[/tex] Final approximate or rounded answer to 2 decimals
The length of AB is the squareroot of 116, or about 10.77 units.
