Question

write the coordinates of the vertices after a reflection over the line x = -5.

Explanation:

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

• Let's assume the coordinates of the vertices are \(C(-4, - 1)\), \(D(-2,-1)\), \(E(-2,0)\), \(F(-4,0)\).
• The formula for reflecting a point \((x,y)\) over the vertical - line \(x = a\) is \((2a - x,y)\). Here \(a=-5\).

1. Calculate the new \(x\) - coordinates for each vertex:

• For point \(C(-4,-1)\):
• Using the formula \(x'=2a - x\), substitute \(a = - 5\) and \(x=-4\). Then \(x'=2\times(-5)-(-4)=-10 + 4=-6\), and \(y'=-1\). So the new coordinates of \(C\) are \((-6,-1)\).
• For point \(D(-2,-1)\):
• Substitute \(a = - 5\) and \(x=-2\) into \(x'=2a - x\). Then \(x'=2\times(-5)-(-2)=-10 + 2=-8\), and \(y'=-1\). So the new coordinates of \(D\) are \((-8,-1)\).
• For point \(E(-2,0)\):
• Substitute \(a = - 5\) and \(x=-2\) into \(x'=2a - x\). Then \(x'=2\times(-5)-(-2)=-10 + 2=-8\), and \(y'=0\). So the new coordinates of \(E\) are \((-8,0)\).
• For point \(F(-4,0)\):
• Substitute \(a = - 5\) and \(x=-4\) into \(x'=2a - x\). Then \(x'=2\times(-5)-(-4)=-10 + 4=-6\), and \(y'=0\). So the new coordinates of \(F\) are \((-6,0)\).

Answer:

The new coordinates of \(C\) are \((-6,-1)\), the new coordinates of \(D\) are \((-8,-1)\), the new coordinates of \(E\) are \((-8,0)\), and the new coordinates of \(F\) are \((-6,0)\).