Question

according to the number line, what is the distance between points a and b?
number line with a at -2, b at 12, and options: 6 units, 7 units, 12 units, 14 units

Explanation:

Step1: Identify coordinates of A and B

Point A is at -2, point B is at 12.

Step2: Calculate distance

Distance between two points \( x_1 \) and \( x_2 \) on number line is \( |x_2 - x_1| \). So \( |12 - (-2)| = |14| = 14 \)? Wait, no, wait. Wait, let's count the units. From -2 to 0 is 2 units, 0 to 12 is 12 units. Total 2 + 12 = 14? Wait no, wait the number line: A is at -2, B is at 12. The difference is 12 - (-2) = 14? But wait the options: 14 is an option. Wait but let me check again. Wait the number line: each tick is 2? Wait no, the numbers are -16, -14, -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12, 14, 16. So the distance between -2 and 12: let's count the intervals. From -2 to 0: 2 units (since -2 to 0 is 2 steps of 1? Wait no, the ticks are at -16, -14, ..., so each tick is 2 units? Wait no, -16 to -14 is 2, so each tick is 2 units? Wait no, the labels are -16, -14, -12, etc., so the distance between each labeled tick is 2. But point A is at -2, which is between -4 and 0? Wait no, the number line has A at -2 (the tick at -2) and B at 12 (the tick at 12). Wait, let's list the positions:

-16, -14, -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12, 14, 16.

So the coordinate of A is -2, coordinate of B is 12. The distance between them is \( |12 - (-2)| = 14 \)? But wait the options include 14 units. Wait but let me check again. Wait maybe I made a mistake. Wait from -2 to 12: how many units? Let's count the number of intervals. From -2 to 0: 2 units (since -2 + 2 = 0). From 0 to 12: 12 units. So total 2 + 12 = 14. Yes, so the distance is 14 units. Wait but the options: 6,7,12,14. So 14 is correct. Wait but wait, maybe the ticks are 1 unit? Wait no, the labels are -16, -14, so each label is 2 units apart. But the points A and B are at -2 and 12, which are labeled ticks? Wait the number line shows A at -2 (the tick with -2) and B at 12 (the tick with 12). So the distance is 12 - (-2) = 14. So the answer is 14 units.

Wait, but let me check again. Maybe I misread the number line. Let's see: the number line has A at -2 and B at 12. The distance between two points on a number line is the absolute difference of their coordinates. So \( |12 - (-2)| = |14| = 14 \). So the distance is 14 units.

Answer:

14 units