Question

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

Explanation:

Step1: Recall distance - formula for translation

The translation is 4 units up and 3 units left. The distance between a point and its translated - point forms the hypotenuse of a right - triangle, where the vertical side (y - direction) has length $a = 4$ and the horizontal side (x - direction) has length $b = 3$.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem for the distance $d$ between two points is $d=\sqrt{a^{2}+b^{2}}$. Substitute $a = 4$ and $b = 3$ into the formula: $d=\sqrt{4^{2}+3^{2}}=\sqrt{16 + 9}=\sqrt{25}=5$.

Answer:

B. 5 units