Question

reflect figure pqrs across the x-axis. reflect each vertex across the x-axis.

Explanation:

Step1: Recall reflection over x - axis rule

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

Step2: Identify coordinates of vertices

First, find the coordinates of vertices \(P\), \(Q\), \(R\), \(S\) from the graph. Let's assume the grid has unit squares.

• Let \(Q=(- 3,2)\), \(R = (-3,4)\), \(P=(-1,2)\), \(S=(-1,4)\) (assuming the x - coordinate of \(Q\) and \(R\) is - 3, \(P\) and \(S\) is - 1, and y - coordinates are 2 and 4 respectively).

Step3: Apply reflection rule to each vertex

• For \(Q(-3,2)\): Using the rule \((x,y)\to(x, - y)\), we get \(Q'(-3,-2)\).
• For \(R(-3,4)\): Using the rule, we get \(R'(-3,-4)\).
• For \(P(-1,2)\): Using the rule, we get \(P'(-1,-2)\).
• For \(S(-1,4)\): Using the rule, we get \(S'(-1,-4)\).

Step4: Plot the reflected vertices

Plot the points \(Q'(-3,-2)\), \(R'(-3,-4)\), \(P'(-1,-2)\), \(S'(-1,-4)\) and then connect them to get the reflected figure \(P'Q'R'S'\).

Answer:

To reflect figure \(PQRS\) across the \(x\) - axis, we use the rule \((x,y)\to(x, - y)\) for each vertex. The reflected vertices are \(P'(-1,-2)\), \(Q'(-3,-2)\), \(R'(-3,-4)\), \(S'(-1,-4)\) and the reflected figure is formed by connecting these points. (The final answer is the set of reflected vertices and the figure formed by them, with the key being the application of the reflection rule over the \(x\) - axis.)