Question

#10: the orourkes found a breakfast restaurant whose location is a reflection across the y - axis of their hotel. what are the coordinates of the restaurant? if each unit on the grid represents one mile, how far is the hotel from the restaurant?

Explanation:

Step1: Determine the hotel's coordinates

From the graph, the hotel's coordinates are \((-5,-2)\).

Step2: Find the reflection across the y - axis

The rule for reflection across the \(y\) - axis is \((x,y)\to(-x,y)\).
For the point \((-5,-2)\), after reflection, the \(x\) - coordinate changes sign. So the restaurant's coordinates are \((5,-2)\).

Step3: Calculate the distance between the hotel and the restaurant

Since the \(y\) - coordinates are the same (\(y=-2\) for both points), we use the distance formula for points \((x_1,y_1)\) and \((x_2,y_2)\) when \(y_1 = y_2\): \(d=\vert x_2 - x_1\vert\).
Here, \(x_1=-5\) and \(x_2 = 5\), so \(d=\vert5-(-5)\vert=\vert5 + 5\vert=10\) miles.

Answer:

The coordinates of the restaurant are \((5,-2)\) and the distance between the hotel and the restaurant is \(10\) miles.