To determine the appropriate [tex]$x$[/tex]-axis and [tex]$y$[/tex]-axis unit scales given the coordinates [tex]\((15, 84)\)[/tex], we must evaluate each given option to see which one fits these coordinates appropriately.
### Option A: [tex]$x$[/tex]-axis: 10, [tex]$y$[/tex]-axis: 2
For this option:
- Check if the x-coordinate 15 fits the scale of the x-axis:
[tex]\[ 15 \div 10 = 1.5 \quad (\text{not an integer, so it doesn't fit}) \][/tex]
- Check if the y-coordinate 84 fits the scale of the y-axis:
[tex]\[ 84 \div 2 = 42 \quad (\text{integer, so it fits}) \][/tex]
In this case, 15 does not fit on a scale of 10, so this option is not valid.
### Option B: [tex]$x$[/tex]-axis: 20, [tex]$y$[/tex]-axis: 10
For this option:
- Check if the x-coordinate 15 fits the scale of the x-axis:
[tex]\[ 15 \div 20 = 0.75 \quad (\text{not an integer, so it doesn't fit}) \][/tex]
- Check if the y-coordinate 84 fits the scale of the y-axis:
[tex]\[ 84 \div 10 = 8.4 \quad (\text{not an integer, so it doesn't fit}) \][/tex]
In this case, neither 15 nor 84 fit on their respective scales, so this option is not valid.
### Option C: [tex]$x$[/tex]-axis: 2, [tex]$y$[/tex]-axis: 10
For this option:
- Check if the x-coordinate 15 fits the scale of the x-axis:
[tex]\[ 15 \div 2 = 7.5 \quad (\text{not an integer, so it doesn't fit}) \][/tex]
- Check if the y-coordinate 84 fits the scale of the y-axis:
[tex]\[ 84 \div 10 = 8.4 \quad (\text{not an integer, so it doesn't fit}) \][/tex]
In this case, neither 15 nor 84 fit on their respective scales, so this option is not valid.
### Option D: [tex]$x$[/tex]-axis: 10, [tex]$y$[/tex]-axis: 20
For this option:
- Check if the x-coordinate 15 fits the scale of the x-axis:
[tex]\[ 15 \div 10 = 1.5 \quad (\text{not an integer, so it doesn't fit}) \][/tex]
- Check if the y-coordinate 84 fits the scale of the y-axis:
[tex]\[ 84 \div 20 = 4.2 \quad (\text{not an integer, so it doesn't fit}) \][/tex]
In this case, neither 15 nor 84 fit on their respective scales, so this option is not valid.
### Conclusion:
None of the given options (A, B, C, or D) appropriately scale both coordinates [tex]\((15, 84)\)[/tex]. Therefore, based on the given information, there is no valid option among the provided choices. The answer is that none of the options A, B, C, or D are appropriate.
