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 is 1 unit. From the graph, \(AB = 5\) units and \(BC=4\) units.

Step2: Apply the Pythagorean theorem

In right - triangle \(ABC\), by the Pythagorean theorem \(AC=\sqrt{AB^{2}+BC^{2}}\). Substitute \(AB = 5\) and \(BC = 4\) into the formula: \(AC=\sqrt{5^{2}+4^{2}}=\sqrt{25 + 16}=\sqrt{41}\approx6.4\).

Since the closest integer to \(6.4\) among common multiple - choice values (assuming options like \(6\), \(7\) etc. are present) is \(6\) (if \(6\) is an option) or \(7\) (if \(6\) is not and \(7\) is). But if we assume standard multiple - choice with \(6\) as an option (as \(6.4\) is closer to \(6\) than to \(7\)).

Answer:

\(6\) (assuming \(6\) is one of the answer choices)