Final answer:
The value -10 is less than 10 because on a number line, negative numbers lie to the left of zero and are always considered less than positive numbers, which lie to the right of zero.
Step-by-step explanation:
The question of why -10 is less than 10 even though both numbers are the same distance from 0 can be explained through the concept of the number line and the direction of numbers. On a number line, negative numbers are placed to the left of zero and positive numbers to the right. The absolute value denotes the distance from 0 without considering direction; thus, -10 and 10 are equidistant from 0. However, in terms of value, any positive number is always greater than any negative number, making -10 less than 10.
When you start a calculation, for instance, determining displacement, you choose a frame of reference and a positive direction. If the reference point is taken to be Komal's house and the positive direction towards Kevin's house, then Komal's displacement is 100 m towards the school. If Komal were to move in the opposite direction, the displacement would be -100 m, indicating a movement away from the reference point, though the distance covered is the same.
It is also analogous to vectors, which are quantities that have both magnitude and direction. A vector of -10 has the same magnitude but opposite direction as a vector of 10. Thus, when it comes to value comparisons on a number line, -10 is less because it lies to the left of 0, and in conventional mathematics, left is always less than right.