Question

1. reflecting the point ((3, -4)) over the (y)-axis results in which coordinates?

a. ((-3, 4))
b. ((-3, -4))
c. ((3, 4))
d. ((3, -4))

Explanation:

Step1: Recall reflection over y - axis rule

The rule for reflecting a point \((x,y)\) over the \(y\) - axis is that the \(x\) - coordinate changes its sign and the \(y\) - coordinate remains the same. So the new coordinates after reflection over the \(y\) - axis are \((-x,y)\).

Step2: Apply the rule to the point \((3,-4)\)

For the point \((3,-4)\), where \(x = 3\) and \(y=-4\). When we reflect it over the \(y\) - axis, the new \(x\) - coordinate is \(-x=-3\) and the new \(y\) - coordinate is \(y = - 4\). So the reflected point has coordinates \((-3,-4)\).

Answer:

b. \((-3,-4)\)