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:

To reflect a point \((x, y)\) over the horizontal line \(y = k\), we use the formula for reflection over a horizontal line: the \(x\)-coordinate remains the same, and the \(y\)-coordinate is transformed as \(y' = 2k - y\). Here, \(k=-3\), so the formula becomes \(y' = 2(-3)-y=-6 - y\), and \(x' = x\).

Step 1: Identify the original points

First, we determine the coordinates of the vertices of the original figure (let's assume the original points are, from the graph, approximately:

• \(A(-7, -9)\)
• \(B(-5, -5)\)
• \(C(-1, -7)\)
• \(D(-5, -9)\)

Step 2: Reflect each point using \(y' = -6 - y\) and \(x' = x\)

For point \(A(-7, -9)\):

• \(x' = -7\)
• \(y' = -6 - (-9)=-6 + 9 = 3\)

Reflected point: \(A'(-7, 3)\)

For point \(B(-5, -5)\):

• \(x' = -5\)
• \(y' = -6 - (-5)=-6 + 5 = -1\)

Reflected point: \(B'(-5, -1)\)

For point \(C(-1, -7)\):

• \(x' = -1\)
• \(y' = -6 - (-7)=-6 + 7 = 1\)

Reflected point: \(C'(-1, 1)\)

For point \(D(-5, -9)\):

• \(x' = -5\)
• \(y' = -6 - (-9)=-6 + 9 = 3\)

Reflected point: \(D'(-5, 3)\)

Step 3: Plot the reflected points

Plot \(A'(-7, 3)\), \(B'(-5, -1)\), \(C'(-1, 1)\), and \(D'(-5, 3)\) on the coordinate plane.

Answer:

The reflected points are \(\boldsymbol{(-7, 3)}\), \(\boldsymbol{(-5, -1)}\), \(\boldsymbol{(-1, 1)}\), and \(\boldsymbol{(-5, 3)}\). Plot these points to form the reflected figure.