Question

1. farrah sketched a map of the inside of the school building. she graphed the point ( p(3, -4) ) for the main office. the lunchroom is located at ( p ), a reflection of ( p ) across the ( y )-axis.

part a what ordered pair represents the location of the lunchroom?
part b plot the point that represents the location of the lunchroom on the coordinate plane.
coordinate plane image with ( x )-axis, ( y )-axis, and origin ( o )

Explanation:

Part A

Step1: Recall reflection over y - axis rule

The rule for reflecting a point \((x,y)\) across the \(y\) - axis is that the new point \((x',y')\) has \(x'=-x\) and \(y' = y\).
For the point \(P(3,-4)\), when we reflect it across the \(y\) - axis, the \(x\) - coordinate changes its sign and the \(y\) - coordinate remains the same.

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

Given \(x = 3\) and \(y=-4\), after reflection across the \(y\) - axis, \(x'=-3\) and \(y'=-4\). So the coordinates of \(P'\) (the lunchroom) are \((-3,-4)\).

Answer:

\((-3,-4)\)

Part B

To plot the point \((-3,-4)\) on the coordinate plane:

1. Start at the origin \((0,0)\).
2. Move 3 units to the left along the \(x\) - axis (because the \(x\) - coordinate is \(- 3\)).
3. Then move 4 units down along the \(y\) - axis (because the \(y\) - coordinate is \(-4\)).
4. Mark the point at this location. (Since we can't draw the actual plot here, the description of the plotting process is as above. If we were to represent it textually on the given grid, we would find the intersection of the vertical line \(x = - 3\) and the horizontal line \(y=-4\) and mark the point there.)