Question

select all the correct answers
which sequences of transformations performed on shape i show its congruency to shape ii?
a reflection across the x - axis, followed by a 90° clockwise rotation about the origin, and then a translation 5 units left
a reflection across the x - axis, followed by a 90° counterclockwise rotation about the origin, and then a translation 5 units right
a reflection across the y - axis, followed by a 90° clockwise rotation about the origin, and then a translation 5 units left
a reflection across the x - axis, followed by a 90° counterclockwise rotation about the origin, and then a translation 5 units left
a reflection across the y - axis, followed by a 90° counterclockwise rotation about the origin, and then a translation 5 units left

Explanation:

Step1: Analyze reflection across x - axis

When a shape is reflected across the \(x\) - axis, the \(y\) - coordinate of each point \((x,y)\) changes to \((x, - y)\).

Step2: Analyze rotation

For a \(90^{\circ}\) counter - clockwise rotation about the origin, the transformation rule for a point \((x,y)\) is \((-y,x)\). After reflection across \(x\) - axis (point \((x,y)\) becomes \((x, - y)\)), a \(90^{\circ}\) counter - clockwise rotation gives \((y,x)\).

Step3: Analyze translation

Translation of 5 units right means adding 5 to the \(x\) - coordinate of each point.

Answer:

a reflection across the \(x\) - axis, followed by a \(90^{\circ}\) counterclockwise rotation about the origin, and then a translation 5 units right.