Question

reflect the point (6, 4) across the y-axis. what are the new coordinates?
options:
○ (-6, -4)
○ (4, 6)
○ (6, -4)
○ (-6, 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. So, 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

The given point is \((6,4)\). Here, \(x = 6\) and \(y = 4\). Using the reflection rule over the \(y\) - axis, we change the sign of the \(x\) - coordinate. So the new \(x\) - coordinate is \(- 6\) and the \(y\) - coordinate remains \(4\). So the new coordinates are \((-6,4)\).

Answer:

D. \((-6,4)\) (assuming the last option is D as per the options given: \(\bigcirc(-6,4)\))