Question

3\\(\triangle xyz\\) is translated 4 units up and 3 units left to yield \\(\triangle xyz\\). what is the distance between any two corresponding points on \\(\triangle xyz\\) and \\(\triangle xyz\\)?\
\\(\bigcirc\\) a. 5 units\
\\(\bigcirc\\) b. 7 units\
\\(\bigcirc\\) c. \\(\sqrt{7}\\) units\
\\(\bigcirc\\) d. 25 units

Explanation:

Step1: Apply the distance formula for translation

The translation can be modeled as a right - triangle. The vertical translation (4 units up) and horizontal translation (3 units left) are the legs of a right - triangle. We use the Pythagorean theorem \(d=\sqrt{a^{2}+b^{2}}\), where \(a = 4\) and \(b=3\).

Step2: Calculate the distance

Substitute \(a = 4\) and \(b = 3\) into the formula: \(d=\sqrt{4^{2}+3^{2}}=\sqrt{16 + 9}=\sqrt{25}=5\).

Answer:

A. 5 units