Question

transformation: reflection

1. using the preimage with vertices h(2, -1), i(1, 4), and j(3, 1), which graph represents the image reflected across y - axis?

reflection across the y - axis
a.
c.
b.
d.

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 reflected coordinates of \(H\), \(I\), \(J\)

• For point \(H(2,-1)\): Using the rule \((x,y)\to(-x,y)\), we substitute \(x = 2\) and \(y=-1\). So the reflected point \(H'\) is \((-2,-1)\).
• For point \(I(1,4)\): Substituting \(x = 1\) and \(y = 4\) into the rule, the reflected point \(I'\) is \((-1,4)\).
• For point \(J(3,1)\): Substituting \(x = 3\) and \(y = 1\) into the rule, the reflected point \(J'\) is \((-3,1)\).

Step3: Match with the graphs

We now look at the options. The graph that has vertices \((-2,-1)\), \((-1,4)\), and \((-3,1)\) is option A.

Answer:

A