Choose the coordinate pair to plot on the coordinate plane so the ratio stays equivalent.

Question

(6,4)

(3,8)

(4,6)

(4,10)

Answer 1

To determine which coordinate pairs maintain an equivalent ratio to (6,4), we need to simplify the coordinate pair to its lowest terms and see if it matches the simplified ratio of the original pair.

First, let's simplify the ratio for the original pair (6,4):
6 ÷ 2 = 3
4 ÷ 2 = 2
The simplified ratio is 3:2.

Now, let's see if any of the given pairs simplify to the same ratio:

1. (3,8) - This pair does not simplify to a ratio of 3:2, and no common factor can simplify 8 to a 2 while simultaneously affecting 3.

2. (4,6) - This pair can be simplified:
4 ÷ 2 = 2
6 ÷ 2 = 3
The simplified ratio is 2:3. Note that this is the reciprocal of 3:2, but it's not the same ratio.

3. (4,10) - This pair cannot simplify to a ratio of 3:2 since there's no common factor that can reduce 10 to 2 while reducing 4 to 3.

None of the given options precisely maintain the equivalent ratio of 3:2 as the original coordinate pair (6,4). If we were strictly looking for a point that would have an equivalent ratio, none of these points would be correct. However, if we consider the reversed ratio 2:3 as equivalent (which it technically isn't in strict terms, but it's the same numbers, just inverted), then (4,6) would be an appropriate choice. Otherwise, we must conclude that no given points maintain an equivalent ratio to (6,4).