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olya-2409 [2.1K]
3 years ago
6

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

Mathematics
1 answer:
Thepotemich [5.8K]3 years ago
7 0

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.

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