Which figure is described below? The locus of points in a plane
equidistant between y = 5 and
y = -3.

A. 1 line
B. 1 plane
C. 2 planes
D. 2 lines

Explanation:

The graph of y = 5 is the horizontal line through 5 on the y axis. Two points on this line are (0,5) and (1,5).

Similarly, the graph of y = -3 is the same idea, but the horizontal line goes through -3 this time. Two points on this line are (0,-3) and (1,-3)

Let's say we're at (0,5). Directly below this point, on the other line, is (0,-3). The midpoint of (0,5) and (0,-3) is (0,1)

The midpoint of (1,5) and (1,-3) is (1,1)

We form a horizontal line through (0,1) and (1,1). This is the locus of points equidistant from the lines y = 5 and y = -3. It's the middle line halfway between the two given lines. Think of it as the median of the highway (the two shoulders of the highway being y = 5 and y = -3).

So that's why the answer is A) 1 line

Side note: any time we have parallel lines like this, the locus of points equidistant from the two lines is always one single line, and it's the median/middle line as described above. This applies to diagonal parallel lines as well, and vertical parallel lines.

step-by-step explanation: