Question

which of the answer choices is closest to the actual distance between point a and point c?

Explanation:

Step1: Determine the lengths of AB and BC

Assume each grid unit is 1. From the graph, \(AB = 6\) (vertical distance) and \(BC = 6\) (horizontal distance).

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is \(AC^{2}=AB^{2}+BC^{2}\). Substitute \(AB = 6\) and \(BC = 6\) into the formula:
\(AC^{2}=6^{2}+6^{2}=36 + 36=72\)
Then \(AC=\sqrt{72}\approx8.49\)

Answer:

8