Question

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

Explanation:

1. First, recall the rule for reflecting a point \((x,y)\) over the line \(x = a\):

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

1. Identify the original - coordinates of the vertices:

• For point \(R(-9,1)\):
• Using the formula \((-2 - x,y)\), substitute \(x=-9\) and \(y = 1\). Then \(-2-(-9)=-2 + 9 = 7\). So the new - coordinate of \(R\) after reflection over \(x=-1\) is \(R'(7,1)\).
• For point \(S(-1,3)\):
• Substitute \(x=-1\) and \(y = 3\) into the formula \((-2 - x,y)\). Then \(-2-(-1)=-2 + 1=-1\). So the new - coordinate of \(S\) after reflection over \(x=-1\) is \(S'(-1,3)\).
• For point \(T(0,0)\):
• Substitute \(x = 0\) and \(y = 0\) into the formula \((-2 - x,y)\). Then \(-2-0=-2\). So the new - coordinate of \(T\) after reflection over \(x=-1\) is \(T'(-2,0)\).
• For point \(Q(-9,-1)\):
• Substitute \(x=-9\) and \(y=-1\) into the formula \((-2 - x,y)\). Then \(-2-(-9)=-2 + 9 = 7\). So the new - coordinate of \(Q\) after reflection over \(x=-1\) is \(Q'(7,-1)\).

Answer:

The coordinates of the vertices after reflection over the line \(x=-1\) are \(R'(7,1)\), \(S'(-1,3)\), \(T'(-2,0)\), \(Q'(7,-1)\)