Question

1. reflect across the y-axis.

Explanation:

Step1: Recall reflection over y - axis rule

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

Step2: Find coordinates of original points

From the graph:

• Point \(A\): Looking at the graph, \(A\) has coordinates \((2,4)\) (since it is 2 units to the right of the \(y\) - axis and 4 units up).
• Point \(B\): \(B\) has coordinates \((4,4)\) (4 units right of \(y\) - axis, 4 units up).
• Point \(C\): \(C\) has coordinates \((5,1)\) (5 units right of \(y\) - axis, 1 unit up).
• Point \(D\): \(D\) has coordinates \((1,1)\) (1 unit right of \(y\) - axis, 1 unit up).

Step3: Apply reflection rule to each point

• For \(A(2,4)\): Using the rule \((x,y)\to(-x,y)\), we get \(A'(- 2,4)\).
• For \(B(4,4)\): Using the rule, we get \(B'(-4,4)\).
• For \(C(5,1)\): Using the rule, we get \(C'(-5,1)\).
• For \(D(1,1)\): Using the rule, we get \(D'(-1,1)\).

Answer:

• \(A(2,4)\to A'(-2,4)\)
• \(B(4,4)\to B'(-4,4)\)
• \(C(5,1)\to C'(-5,1)\)
• \(D(1,1)\to D'(-1,1)\)