To find the distance between points [tex]\( X = -7 \)[/tex] and [tex]\( Y = 3 \)[/tex] using the ruler postulate, follow these steps:
1. Understand the ruler postulate: The ruler postulate states that the distance between two points on a number line is the absolute value of the difference of their coordinates.
2. Identify the coordinates: The coordinates of the points are:
- [tex]\( X = -7 \)[/tex]
- [tex]\( Y = 3 \)[/tex]
3. Calculate the difference between the coordinates:
[tex]\[
Y - X = 3 - (-7)
\][/tex]
4. Simplify the expression:
[tex]\[
3 - (-7) = 3 + 7 = 10
\][/tex]
5. Apply the absolute value: Since we're looking for the distance, we take the absolute value of the difference. In this case, the difference is already positive:
[tex]\[
\text{Distance} = |10| = 10
\][/tex]
So, the distance between points [tex]\( X = -7 \)[/tex] and [tex]\( Y = 3 \)[/tex] is [tex]\( 10 \)[/tex].
Thus, the correct answer is [tex]\( 10 \)[/tex].
