Question

in the diagram, k and k are congruent.
which of the following is a way of transforming k into k?

• a reflection across the x - axis, then a translation down 2 units
• a reflection across the y - axis, then a reflection across the line y = 2
• a clockwise rotation of 90° about the point (0, 2)
• a rotation of 180° about the origin

question 10
1 pts
which of the following is the correct mapping for shape a (quadrant i) to shape b (quadrant ii)?

Explanation:

Step1: Analyze each option

• Option 1: Reflecting over x - axis and translating down 2 units. Visually, the orientation and position don't match this transformation.
• Option 2: Reflecting over y - axis then over \(y = 2\). The final position and orientation don't align with the figure.
• Option 3: Rotating 90° clockwise about \((0,2)\). The shape's orientation after this rotation won't match \(K'\).
• Option 4: Rotating 180° about the origin. A 180° rotation about the origin changes \((x,y)\) to \((-x,-y)\). Looking at the figures, \(K\) and \(K'\) are symmetric with respect to a 180° rotation about the origin.

Answer:

a rotation of \(180^\circ\) about the origin