Question

reflect the figure over the line $y = 3$. plot all of the points of the reflected figure. you may click a plotted point to delete it.

Explanation:

Step1: Identify original points

The original triangle has vertices at \((-8, 9)\), \((-3, 9)\), and \((-6, 6)\).

Step2: Reflect over \(y = 3\)

For a point \((x, y)\), the reflection over \(y = k\) is \((x, 2k - y)\). Here, \(k = 3\), so the formula is \((x, 6 - y)\).

• For \((-8, 9)\): \(y' = 6 - 9 = -3\), so reflected point is \((-8, -3)\).
• For \((-3, 9)\): \(y' = 6 - 9 = -3\), so reflected point is \((-3, -3)\).
• For \((-6, 6)\): \(y' = 6 - 6 = 0\), so reflected point is \((-6, 0)\).

Step3: Plot reflected points

Plot \((-8, -3)\), \((-3, -3)\), and \((-6, 0)\) on the graph.

Answer:

The reflected triangle has vertices at \((-8, -3)\), \((-3, -3)\), and \((-6, 0)\) (plot these points on the coordinate plane).