Question

if the point (6, −3) is reflected over the y-axis, what are the new coordinates?
○ a. (−6, 3)
○ b. (−6, −3)
○ c. (3, −6)
○ d. (6, 3)

Explanation:

Step1: Recall reflection over y - axis rule

The rule for reflecting a point \((x,y)\) over the \(y\) - axis is that the new \(x\) - coordinate is the negative of the original \(x\) - coordinate, and the \(y\) - coordinate remains the same. In formula terms, if we have a point \((x,y)\), after reflection over the \(y\) - axis, it becomes \((-x,y)\).

Step2: Apply the rule to the given point

The given point is \((6,-3)\). Here, \(x = 6\) and \(y=-3\). Using the reflection rule over the \(y\) - axis, the new \(x\) - coordinate is \(-x=-6\) and the new \(y\) - coordinate is \(y = - 3\). So the new coordinates are \((-6,-3)\).

Answer:

b. \((-6,-3)\)