Question

write the coordinates of the vertices after a reflection over the line y = -6.

Explanation:

1. First, identify the original coordinates of the vertices:

• Let's assume the coordinates of point \(A=(1, - 2)\), point \(B=(5,-2)\), and point \(C=(1,-6)\) from the graph.
• The formula for reflecting a point \((x,y)\) over the horizontal - line \(y = k\) is \((x,2k - y)\). Here, \(k=-6\).

1. Calculate the new coordinates for point \(A\):

• For point \(A=(x_1,y_1)=(1, - 2)\), using the formula \((x,2k - y)\), we substitute \(x = 1\), \(k=-6\), and \(y=-2\).
• \(2k - y=2\times(-6)-(-2)=-12 + 2=-10\).
• So the new coordinates of \(A\) are \((1,-10)\).

1. Calculate the new coordinates for point \(B\):

• For point \(B=(x_2,y_2)=(5,-2)\), substitute \(x = 5\), \(k=-6\), and \(y=-2\) into the formula \((x,2k - y)\).
• \(2k - y=2\times(-6)-(-2)=-12 + 2=-10\).
• So the new coordinates of \(B\) are \((5,-10)\).

1. Calculate the new coordinates for point \(C\):

• For point \(C=(x_3,y_3)=(1,-6)\), substitute \(x = 1\), \(k=-6\), and \(y=-6\) into the formula \((x,2k - y)\).
• \(2k - y=2\times(-6)-(-6)=-12 + 6=-6\).
• So the new coordinates of \(C\) are \((1,-6)\).

Answer:

The coordinates of \(A\) after reflection are \((1,-10)\), the coordinates of \(B\) after reflection are \((5,-10)\), and the coordinates of \(C\) after reflection are \((1,-6)\).