Question

write the coordinates of the vertices after a reflection over the y - axis.

Explanation:

1. Recall the rule for reflecting a point over the \(y\) - axis:

• The rule for reflecting a point \((x,y)\) over the \(y\) - axis is \((x,y)\to(-x,y)\).

1. Identify the original coordinates of the vertices:

• Let's assume the coordinates of point \(F\) are \((- 5,1)\), the coordinates of point \(G\) are \((-1,1)\), and the coordinates of point \(H\) are \((-6,-2)\).

1. Apply the reflection rule:

• For point \(F(-5,1)\):
• Using the rule \((x,y)\to(-x,y)\), when \(x = - 5\) and \(y = 1\), the new \(x\) - coordinate is \(-(-5)=5\) and the \(y\) - coordinate remains \(1\). So the new coordinates of \(F\) are \((5,1)\).
• For point \(G(-1,1)\):
• When \(x=-1\) and \(y = 1\), the new \(x\) - coordinate is \(-(-1) = 1\) and the \(y\) - coordinate remains \(1\). So the new coordinates of \(G\) are \((1,1)\).
• For point \(H(-6,-2)\):
• When \(x=-6\) and \(y=-2\), the new \(x\) - coordinate is \(-(-6)=6\) and the \(y\) - coordinate remains \(-2\). So the new coordinates of \(H\) are \((6,-2)\).

Answer:

The coordinates of \(F\) after reflection over the \(y\) - axis are \((5,1)\), the coordinates of \(G\) after reflection over the \(y\) - axis are \((1,1)\), and the coordinates of \(H\) after reflection over the \(y\) - axis are \((6,-2)\).