Question

line segment (overline{op}) has a length of 2 units and has been plotted on a coordinate plane. if (overline{op}) is rotated (90^{circ}) about the origin and translated 3 units to the right to form (overline{op}), what is the measure of the length of (overline{op})?

Explanation:

Step1: Recall the properties of rotation and translation

Rotation and translation are rigid transformations. Rigid transformations preserve the length of a line segment.

Step2: Apply the property to the problem

Since \(\overline{OP}\) is transformed by rotation (which is a rigid transformation, preserves length) and translation (which is also a rigid transformation, preserves length), the length of \(\overline{O'P'}\) is the same as the length of \(\overline{OP}\).

Answer:

\(2\) units