Question

triangle trs is rotated about point x, resulting in triangle bac. if ab = 10 ft, ac = 14 ft, and bc = 20 ft, what is rs? 10 ft 14 ft 20 ft 24 ft figure may not be drawn to scale

Explanation:

Step1: Recall the property of rotation

Rotation is a rigid transformation. Rigid transformations (rotations, translations, reflections) preserve the lengths of the sides of a figure. So, if \(\triangle TRS\) is rotated about point \(X\) to get \(\triangle BAC\), then \(\triangle TRS\cong\triangle BAC\).

Step2: Identify the corresponding sides

In congruent triangles, corresponding sides are equal. Since \(RS\) corresponds to \(AC\) (by the congruence of \(\triangle TRS\) and \(\triangle BAC\) from the rotation transformation).

Answer:

\(14\mathrm{ft}\) (the second option)