Question

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. Mathematically, if we have a point \((x,y)\), after reflection over the \(y\) - axis, the new point is \((-x,y)\).

Step2: Apply the rule to the given point

We are given the point \((3,-4)\). Here, \(x = 3\) and \(y=-4\). Applying the reflection over \(y\) - axis rule, we change the sign of \(x\) (so \(x\) becomes \(- 3\)) and keep \(y\) the same ( \(y=-4\)). So the reflected point is \((-3,-4)\).

Answer:

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