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.

Explanation:

Step1: Recall the rule for reflection over the x - axis

When a point \((x,y)\) is reflected over the \(x\) - axis, the rule is \((x,y)\to(x, - y)\).
For point \(Q(-5,-1)\):
Using the rule \((x,y)\to(x, - y)\), we substitute \(x=-5\) and \(y = - 1\).
\(Q'(-5,1)\)
For point \(R(-1,-1)\):
Substitute \(x=-1\) and \(y=-1\) into the rule \((x,y)\to(x, - y)\)
\(R'(-1,1)\)
For point \(S(-1,-3)\):
Substitute \(x=-1\) and \(y = - 3\) into the rule \((x,y)\to(x, - y)\)
\(S'(-1,3)\)
For point \(T(-6,-3)\):
Substitute \(x=-6\) and \(y=-3\) into the rule \((x,y)\to(x, - y)\)
\(T'(-6,3)\)

Answer:

Original Point	Points after reflection over \(x\) - axis
\(R(-1,-1)\)	\(R'(-1,1)\)
\(S(-1,-3)\)	\(S'(-1,3)\)
\(T(-6,-3)\)	\(T'(-6,3)\)