Question

in the figure below, a right - angled triangle is located in an xy - plane. what is the approximate distance between the two points a and b, to the nearest tenth? a 3.0 b 6.4 c 6.8 d 9.2 e 20

Explanation:

Step1: Find the lengths of \(BC\) and \(AC\)

For \(BC\): \(x\)-coordinates of \(B(1,3)\) and \(C\) (since \(C\) has the same \(y\)-coordinate as \(B\) and \(x\)-coordinate as \(A\)): \(BC=\vert5 - 1\vert=4\)
For \(AC\): \(y\)-coordinates of \(A(5,8)\) and \(C\) (since \(C\) has the same \(x\)-coordinate as \(A\) and \(y\)-coordinate as \(B\)): \(AC=\vert8 - 3\vert=5\)

Step2: Apply the Pythagorean theorem

By the Pythagorean theorem \(AB=\sqrt{BC^{2}+AC^{2}}\)
Substitute \(BC = 4\) and \(AC = 5\) into the formula: \(AB=\sqrt{4^{2}+5^{2}}=\sqrt{16 + 25}=\sqrt{41}\approx6.4\)

Answer:

B. 6.4