Question

write the coordinates of the vertices after a reflection over the line x = -1.

Explanation:

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

• Let's assume the vertices \(E(0, - 2)\), \(B(1,-3)\), \(C(8,-2)\) (estimated from the graph).

1. Recall the rule for reflection over the line \(x = a\):

• The rule for reflecting a point \((x,y)\) over the line \(x=a\) is \((2a - x,y)\). Here \(a=-1\).

1. Calculate the new - coordinates for each vertex:

• For point \(E(0,-2)\):
• Using the formula \((2a - x,y)\) with \(a = - 1\) and \(x = 0,y=-2\), we have \(2\times(-1)-0=-2\), and \(y=-2\). So the new coordinates of \(E\) are \(E'(-2,-2)\).
• For point \(B(1,-3)\):
• Substitute \(a=-1\), \(x = 1\), and \(y=-3\) into the formula \((2a - x,y)\). Then \(2\times(-1)-1=-2 - 1=-3\), and \(y=-3\). So the new coordinates of \(B\) are \(B'(-3,-3)\).
• For point \(C(8,-2)\):
• Substitute \(a=-1\), \(x = 8\), and \(y=-2\) into the formula \((2a - x,y)\). Then \(2\times(-1)-8=-2 - 8=-10\), and \(y=-2\). So the new coordinates of \(C\) are \(C'(-10,-2)\).

Answer:

The coordinates of the vertices after reflection over the line \(x=-1\) are \(E'(-2,-2)\), \(B'(-3,-3)\), \(C'(-10,-2)\) (assuming original vertices were \(E(0, - 2)\), \(B(1,-3)\), \(C(8,-2)\)).