Question

describe the transformation. a. reflection across the line y = x b. reflection across the x - axis c. translation 4 units to the right d. reflection across the y - axis

Explanation:

• Option A: Reflection across \(y = x\) swaps \(x\) and \(y\) coordinates. The figure does not show this swap - like symmetry.
• Option B: Reflection across the \(x\) - axis changes the \(y\) - coordinate sign (\((x,y)\to(x, - y)\)). This is not the case here.
• Option C: Translation 4 units right would move every point of the figure 4 units along the positive \(x\) - axis. But the figure's orientation relative to the axes (left - right symmetry) is not a translation.
• Option D: Reflection across the \(y\) - axis changes the \(x\) - coordinate sign (\((x,y)\to(-x,y)\)). If we consider a point \((x,y)\) on the left - hand triangle, its corresponding point on the right - hand triangle is \((-x,y)\) (for example, if a vertex of the left - hand triangle is \((- 3,5)\), a vertex of the right - hand triangle is \((3,5)\)). This satisfies the reflection across the \(y\) - axis rule.

Answer:

D. reflection across the \(y\) - axis