Question

problems 10 - 12: spiral review
determine whether each transformations moves triangle xyz onto triangle xyz. choose true or false.
triangle xyz is reflected across the y - axis, followed by a reflection across the x - axis.
triangle xyz is reflected across the x - axis, followed by a reflection across the y - axis.
triangle xyz is reflected across the x - axis, followed by a translation 3 units left.

Explanation:

Step1: Recall reflection rules

Reflection across y - axis changes (x,y) to (-x,y). Reflection across x - axis changes (x,y) to (x, - y).

Step2: Analyze first transformation

If we reflect triangle XYZ across the y - axis, then across the x - axis. Let a point (x,y) on triangle XYZ first become (-x,y) after y - axis reflection and then (-x,-y) after x - axis reflection. The orientation and position do not match triangle X'Y'Z', so it's false.

Step3: Analyze second transformation

If we reflect across the x - axis first, (x,y) becomes (x, - y), then across the y - axis it becomes (-x,-y). The orientation and position do not match triangle X'Y'Z', so it's false.

Step4: Analyze third transformation

If we reflect across the x - axis, (x,y) becomes (x, - y). Then translating 3 units left changes (x, - y) to (x - 3,-y). The orientation and position do not match triangle X'Y'Z', so it's false.

Answer:

False
False
False