Question

graph the image of square pqrs after a reflection over the y - axis.

Explanation:

Step1: Find coordinates of original square

Assume coordinates of \(P(3, - 4)\), \(Q(7,-4)\), \(R(7, - 1)\), \(S(3,-1)\) (from the graph).

Step2: Apply reflection rule over \(y\) - axis

The rule for reflection over \(y\) - axis is \((x,y)\to(-x,y)\).
For \(P(3, - 4)\), after reflection \(P'(-3,-4)\).
For \(Q(7,-4)\), after reflection \(Q'(-7,-4)\).
For \(R(7, - 1)\), after reflection \(R'(-7,-1)\).
For \(S(3,-1)\), after reflection \(S'(-3,-1)\).

Step3: Plot the new points

Plot \(P'(-3,-4)\), \(Q'(-7,-4)\), \(R'(-7,-1)\), \(S'(-3,-1)\) on the coordinate plane and connect them to form the reflected square.

Answer:

Plot the points \(P'(-3,-4)\), \(Q'(-7,-4)\), \(R'(-7,-1)\), \(S'(-3,-1)\) and connect them.