Question

when finding abosolute value in a coordinate plane if there are 2 pairs one you are finding the absolute value of the x-coordinate do you add when they are in the same quadtient

Answer 1

Use the absolute difference: distance along the x-direction between two points (x1,y1) and (x2,y2) is |x2 − x1|. You do not always “add” the x-values.

Rules and examples:
- If both x-coordinates are positive and x2 > x1, |x2 − x1| = x2 − x1 (you subtract, not add).
Example: x = 3 and x = 7 → |7 − 3| = 4.
- If both x-coordinates are negative, |x2 − x1| = |(more negative) − (less negative)| which again is a subtraction of their values (in effect the difference of their absolute values).
Example: x = −3 and x = −7 → |−7 − (−3)| = |−4| = 4.
- If the x-coordinates have opposite signs (one left of the y-axis, one right), then |x2 − x1| equals the sum of their absolute values.
Example: x = −3 and x = 7 → |7 − (−3)| = |10| = 10 = |7| + |−3|.

Remember: the general 2‑D distance formula is sqrt((x2 − x1)^2 + (y2 − y1)^2), and the x-part of that is |x2 − x1|.