Question

question 7. describe the transformation. a. reflection across the line y = x b. reflection across the x - axis c. reflection across the y - axis d. reflection across y = - 1 e. translation 2 units down

Explanation:

A reflection across the \(x -\)axis would invert the figure vertically (flip it over the \(x -\)axis). A reflection across the \(y -\)axis would invert the figure horizontally (flip it over the \(y -\)axis). A reflection across \(y=x\) would swap the \(x\) and \(y\) coordinates of points. A reflection across \(y =-1\) is a vertical reflection over the line \(y=-1\). A translation 2 units down would move the figure 2 units in the negative \(y -\)direction without flipping.

Looking at the given figure, the upper - case "A" and lower - case "a" (assuming the two figures) are mirror images with respect to the \(x -\)axis. When we reflect a point \((x,y)\) across the \(x -\)axis, it transforms to the point \((x, - y)\).

Answer:

B. Reflection across the x - axis