Question

which of the following transformations carry the isosceles trapezoid onto itself?
rotation of 90° counterclockwise
rotation of 180° counterclockwise
reflection across ( l_2 )
reflection across ( l_1 )

Explanation:

Step1: Analyze rotation of \(90^{\circ}\) counter - clockwise

An isosceles trapezoid is not symmetric about a \(90^{\circ}\) rotation. After a \(90^{\circ}\) counter - clockwise rotation, the shape will not map onto itself.

Step2: Analyze rotation of \(180^{\circ}\) counter - clockwise

An isosceles trapezoid is not a centrally symmetric figure (except for some special cases which are not the general isosceles trapezoid). A \(180^{\circ}\) counter - clockwise rotation will not map the trapezoid onto itself.

Step3: Analyze reflection across \(l_{2}\)

A reflection across \(l_{2}\) will not map the isosceles trapezoid onto itself as \(l_{2}\) is not a line of symmetry for an isosceles trapezoid.

Step4: Analyze reflection across \(l_{1}\)

An isosceles trapezoid has a line of symmetry along the vertical line that is equidistant from the two parallel sides (in this case \(l_{1}\)). A reflection across \(l_{1}\) (the vertical line of symmetry) will map the isosceles trapezoid onto itself.

Answer:

reflection across \(l_{1}\)