Question

a contractor is presenting the floor plan for a house.
the client likes the shape and size, but wants the whole thing flipped along a line running east - west through the center of the property.
which of the following choices shows the requested house position?
the positive direction on the y - axis is north. the center of the property is located at the origin on the coordinate plane.

Explanation:

Step1: Understand the Reflection Axis

An east - west line through the origin is the x - axis (since east - west is horizontal, corresponding to the x - axis in the coordinate plane). Reflecting a figure over the x - axis changes the sign of the y - coordinate of each point \((x,y)\) to \((x, - y)\).

Step2: Analyze the Original Figure

The original house (in the top graph) has points with positive y - coordinates (above the x - axis). After reflection over the x - axis, all these points should have negative y - coordinates (below the x - axis), and the shape should be a mirror image across the x - axis.

Step3: Compare with Options

• Look at the four options. We need to find the figure that is the reflection of the original over the x - axis. The original figure has a "step" on the right side (positive x - side) above the x - axis. After reflection, the "step" should be on the right side below the x - axis, and the overall shape should be symmetric with respect to the x - axis.
• By visually inspecting the options, the bottom - left option (the third option if we consider the four options in a 2x2 grid, but looking at the circles, the one with the figure that is the reflection over the x - axis) shows the correct reflection. Wait, actually, let's re - examine. The original figure: when we reflect over the x - axis, the part above the x - axis (positive y) will go below (negative y) and vice - versa. Looking at the options, the option with the figure that is the mirror image across the x - axis (the one where the top part of the original is now the bottom part with y - coordinates negated) is the correct one. Among the four options, the one with the blue and black figures where the black is the original (above x - axis) and blue is the reflection (below x - axis) with the correct shape. The correct option is the one where the reflected figure has the same x - coordinates but y - coordinates flipped. So the figure that is the reflection over the x - axis (east - west line through origin) is the bottom - left option (the third option in the circle - marked ones? Wait, the circles are on the left of each figure. Let's see: the first figure (top - left) has a wrong shape, the second (top - right) is not a reflection, the third (bottom - left) is the reflection over x - axis, and the fourth (bottom - right) is not. So the correct one is the bottom - left option (the one with the circle on the left of the bottom - left figure).

Answer:

The bottom - left figure (the third option when considering the four figures in a 2x2 arrangement, with the circle to the left of it)