Question

question 5 (multiple choice worth 1 points) (03.02r mc) which set of transformations would prove δqrs ~ δuts? reflect δuts over y = 2, and dilate δuts by a scale factor of 2 from point s. reflect δuts over y = 2, and translate δuts by the rule (x + 2, y + 0) translate δuts by the rule (x + 0, y + 6), and reflect δuts over y = 6. translate δuts by the rule (x − 2, y + 0), and reflect δuts over y = 2.

Explanation:

Step1: Recall similarity conditions

Similarity of triangles can be proved by dilation (a similarity transformation). Dilation changes the size but not the shape of the figure.

Step2: Analyze the options

• Option 1: Translation and reflection (rigid motions) make congruent figures, not similar (unless scale factor 1).
• Option 2: Translation and reflection (rigid motions) make congruent figures.
• Option 3: Reflection (rigid motion) and translation (rigid motion) make congruent figures.
• Option 4: Reflection (rigid motion) and dilation (similarity transformation). Dilation with scale factor \(k = 2\) from point \(S\) will map \(\triangle UTS\) to \(\triangle QRS\) (since \(QS = 2US\), \(RS=2TS\) as per the grid - based lengths).

Answer:

Reflect \(\triangle UTS\) over \(y = 2\), and dilate \(\triangle U'T'S'\) by a scale factor of \(2\) from point \(S\).