Answer:
(a) Segments AB and De are not congruent since their lengths are not equal.
(b) Yes, you get the same result. In both cases you must take the absolute value of the difference of the coordinates giving you the same result no matter in which order you subtract the coordinates of the points.
Explanation:
(a)
To find the distance between any two points on the number line, take the absolute value of the difference of the coordinates of the points.
The coordinate of point P is p. The coordinate of point Q is q. PQ or QP, the distance between points P and Q, is:
PQ = QP = |p - q| = |q - p|
It does not make a difference in which order you find the diffeence of the coordinates.
Look at points A and B.
Point A has coordinate -2.
Point B has coordinate 3.
AB = |-2 - 3| = |-5| = 5
Now look at points D and E.
Point D has coordinate 10.
Point E has coordinate 14.
DE = |10 - 14| = |-4| = 4
AB = 5; DE = 4
Answer: The lengths of segments AB and DE are not equal, so the segments are not congruent.
(b)
The coordinate of point A is -2.
The coordinate of point C is 5.
AC = |-2 - 5| = |-7| = 7
If you subtract -2 from 5, and then take the absolute value, you get:
AC = |5 - (-2)| = |5 + 2| = |7| = 7
Again you get 7. The order in which you subtract the coordinates of the points does not affect the result since you take the absolute value of the difference in both cases.
AC =