Question

if the following point were reflected across the y-axis, what would be the coordinates of the reflected point?
(-5, -4)

a (5, -4)

b (5, 4)

c (-5, -5)

d (-5, 4)

Explanation:

Step1: Recall reflection over y - axis rule

The rule for reflecting a point \((x,y)\) across the \(y\) - axis is that the \(y\) - coordinate remains the same and the \(x\) - coordinate changes its sign. 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 \((-5,-4)\). Here, \(x=-5\) and \(y = - 4\).
Using the reflection rule over the \(y\) - axis, the new \(x\) - coordinate is \(-(-5)=5\) and the \(y\) - coordinate remains \(-4\). So the reflected point is \((5,-4)\).

Answer:

a. \((5, - 4)\)