Question

which sequence of transformations maps triangle abc onto triangle a\b\c\? * 1 point rotation 180 degrees about the origin followed by a translation up 1 unit reflection over the y - axis followed by a rotation 90 about point c rotation 90 degrees about point c followed by a reflection over the y - axis reflection over the x - axis followed by a translation up 2 units

Explanation:

Step1: Analyze reflection over y - axis

When reflecting a point $(x,y)$ over the y - axis, the transformation is $(x,y)\to(-x,y)$. If we reflect $\triangle ABC$ over the y - axis, the orientation of the triangle changes with respect to the y - axis.

Step2: Analyze rotation about point C

A 90 - degree rotation about a point C changes the orientation of the reflected triangle to match $\triangle A''B''C''$. If we first reflect over the y - axis and then rotate 90 degrees about point C, we can map $\triangle ABC$ onto $\triangle A''B''C''$.

Step3: Check other options

• For a 180 - degree rotation about the origin followed by a translation up 1 unit, the orientation and position won't match.
• For a 90 - degree rotation about point C followed by a reflection over the y - axis, the order of operations will not give the correct mapping.
• For a reflection over the x - axis followed by a translation up 2 units, the orientation and position won't match the target triangle.

Answer:

Reflection over the y - axis followed by a rotation 90 about point C