Answer:
Approximate length of AB is 9.2 units.
Step-by-step explanation:
You can use Pythagorean Theorem (check out the picture below) or directly use the distance formula.
Pythagorean Theorem
[tex]\text{hypotenuse}^2 = \text{leg}_1^2 + \text{leg}_2^2[/tex]
Hypotenuse is AB and you can read the length of the legs from the graph.
[tex]\text{AB}^2 = 6^2 + 7^2\\\text{AB}^2 = 85\\\text{AB} = \sqrt{85} \approx 9.2195\\\text{AB} \approx 9.2[/tex]
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Another way to do it is to use the distance formula.
The Distance Formula
[tex]\text{The distance between two points } (x_1, y_1) \text{ and } (x_2, y_2) \text{ is given by the formula:}\\d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]
You can read the points from the graph:
A(-2,-3)
B(4,4)
[tex]d = \sqrt{(-2-4)^2 + (-3-4)^2}\\d = \sqrt{36 + 49}\\d = \sqrt{85} \approx 9.2[/tex]
You can see that both ways give the same answer. Use whatever you prefer.
