Question

reflect quadrilateral qrst over the x - axis. then, reflect its image, quadrilateral ( qrst ), over the y - axis. start by reflecting the vertices, q, r, s, and t, of quadrilateral qrst over the x - axis. original point: q (1,1), r (1,5), s (3,7), t (3,1). points after reflection over x - axis: ( q ), ( r ), ( s ), ( t )

Explanation:

Step1: Recall reflection over x - axis rule

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

Step2: Apply the rule to each point

• For point \(Q(1,1)\): Using the rule \((x,y)\to(x, - y)\), we get \(Q'(1,-1)\) since \(x = 1\) and \(y=1\), and \(-y=-1\).
• For point \(R(1,5)\): Using the rule \((x,y)\to(x, - y)\), we get \(R'(1,-5)\) since \(x = 1\) and \(y = 5\), and \(-y=-5\).
• For point \(S(3,7)\): Using the rule \((x,y)\to(x, - y)\), we get \(S'(3,-7)\) since \(x = 3\) and \(y = 7\), and \(-y=-7\).
• For point \(T(3,1)\): Using the rule \((x,y)\to(x, - y)\), we get \(T'(3,-1)\) since \(x = 3\) and \(y = 1\), and \(-y=-1\).

Answer:

Original Point	Points after reflection over \(x\) - axis
\(R(1,5)\)	\(R'(1,-5)\)
\(S(3,7)\)	\(S'(3,-7)\)
\(T(3,1)\)	\(T'(3,-1)\)