Question

figure c and figure y: dilation with scale factor $\frac{1}{2}$ and center of dilation $(0, 0)$, followed by a reflection across the $x$-axis
figure c and figure l: dilation with scale factor of $\frac{1}{2}$ and center of dilation $(0, 0)$, followed by a reflection across the $x$-axis
figure g and figure l: dilation with scale factor $\frac{1}{4}$ and center of dilation $(0, 0)$, followed by a translation 1 unit left and 2 units down
figure g and figure y: dilation with a scale factor of $\frac{1}{4}$ and center of dilation $(0, 0)$, followed by a translation 1 unit left and 2 units down
figure l and figure y: dilation with scale factor $\frac{1}{3}$ and center of dilation $(0, 0)$, following by a reflection across the $y$-axis

Explanation:

To solve this, we analyze each option by recalling transformation rules (dilation, reflection, translation):

Option 1: Figure C and Figure Y

• Dilation: Scale factor \(\frac{1}{2}\), center \((0,0)\) reduces size by half.
• Reflection over \(x\)-axis: \((x,y) \to (x,-y)\).

If Figure C, after dilation and reflection, matches Figure Y, this could be valid.

Option 2: Figure C and Figure L

• Same dilation/reflection as Option 1. But Figure L’s position/shape likely differs from Figure Y, so this is inconsistent.

Option 3: Figure G and Figure L

• Dilation: Scale factor \(\frac{1}{4}\) (too small, as \(\frac{1}{4}\) would shrink drastically).
• Translation: 1 left, 2 down. Unlikely to match, as scale factor is incorrect.

Option 4: Figure G and Figure Y

• Dilation: Scale factor \(\frac{1}{4}\) (incorrect, as \(\frac{1}{4}\) is too small for typical transformations between these figures).
• Translation: 1 left, 2 down. Scale factor mismatch.

Option 5: Figure L and Figure Y

• Dilation: Scale factor \(\frac{1}{3}\) (unusual, and reflection over \(y\)-axis: \((x,y) \to (-x,y)\)). This does not align with typical transformations between L and Y.

The most consistent transformation is Option 1 (Figure C and Figure Y: dilation with scale factor \(\frac{1}{2}\) and center \((0,0)\), followed by reflection across \(x\)-axis).

Answer:

A. Figure C and Figure Y: dilation with scale factor \(\boldsymbol{\frac{1}{2}}\) and center of dilation \((0, 0)\), followed by a reflection across the \(x\)-axis