Answer:
Approximate length of AB is 9.2 units.
Explanation:
You can use Pythagorean Theorem (check out the picture below) or directly use the distance formula.
Pythagorean Theorem
![\text{hypotenuse}^2 = \text{leg}_1^2 + \text{leg}_2^2](https://img.qammunity.org/2023/formulas/mathematics/high-school/x1w9wtmnjfy8i1xh6fzdsjrj83oo94u30b.png)
Hypotenuse is AB and you can read the length of the legs from the graph.
![\text{AB}^2 = 6^2 + 7^2\\\text{AB}^2 = 85\\\text{AB} = √(85) \approx 9.2195\\\text{AB} \approx 9.2](https://img.qammunity.org/2023/formulas/mathematics/college/tswj29zt9mftjjm4iymxuwokx3aodke6el.png)
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Another way to do it is to use the distance formula.
The Distance Formula
![\text{The distance between two points } (x_1, y_1) \text{ and } (x_2, y_2) \text{ is given by the formula:}\\d = √((x_2-x_1)^2 + (y_2-y_1)^2)](https://img.qammunity.org/2023/formulas/mathematics/college/gfmfctpb9ap48yl046pgen832obivr0p14.png)
You can read the points from the graph:
A(-2,-3)
B(4,4)
![d = √((-2-4)^2 + (-3-4)^2)\\d = √(36 + 49)\\d = √(85) \approx 9.2](https://img.qammunity.org/2023/formulas/mathematics/college/hduskh2j1twmhgxlgwnxexicq82lclbc7x.png)
You can see that both ways give the same answer. Use whatever you prefer.