Which point represents the unit rate?

On a coordinate plane, point A is (0, 1), point B is (1, 0), point C is (1, 0.5), and point D is (2, 1).

A
B
C
D

1 answer

To find the point that represents the unit rate, we need to identify which point corresponds to a ratio of 1:1. In coordinate terms, a unit rate is where the two quantities represented on the axes are equal, typically expressed as (x, y) where x = y.

Let's analyze the given points:

  • Point A: (0, 1) - Here, y ≠ x
  • Point B: (1, 0) - Here, y ≠ x
  • Point C: (1, 0.5) - Here, y ≠ x
  • Point D: (2, 1) - Here, 1 is half of 2; thus, y < x

None of the points specifically show a ratio of 1:1 (where x would equal y), hence they don't represent a unit rate.

However, if we're looking for the ratio that represents the "output" for "1 unit" of the "input," we can consider Point D: (2, 1). This indicates that for every 2 units of the first quantity (the x-value), there is 1 unit of the second quantity (the y-value), which could represent a unit rate of 0.5.

To clarify, based on the standard expectation of a "unit rate" definition as x:y = 1, the correct answer is technically none of these points shows direct x = y.

If you are interpreting "unit rate" in terms of an output relative to an input (like points represented in a practical context), Point D (2, 1) might suggest a half-unit rate or a 1:2 relationship, which might be where that interpretation comes in context.

So the final answer, if strictly referring to unit rates as x = y, would be none are unit rates. Otherwise, for unit output relationships, D might be the best call.