Question

Alan found the distance between point A(-8, -4) and point B(3, -4). His worn is shown below. -8 to the y-axis=8 units. 3 to the y-axis=3 units. |-8| - |3| = 5 units from A to B. What error did Alan make? What is the actual distance from point A to point B?

Answer 1

Explanation:

Alan made an error in assuming that the distance between -8 and 3 on the x-axis is the same as the distance between -8 and the y-axis, and between 3 and the y-axis. This is not necessarily true, as the distance between two points on a coordinate plane is given by the Pythagorean theorem:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Using this formula, we can find the actual distance between points A and B:

distance = sqrt((3 - (-8))^2 + (-4 - (-4))^2)

distance = sqrt(11^2 + 0^2)

distance = sqrt(121)

distance = 11

So the actual distance between points A and B is 11 units.

Therefore, Alan's error was assuming that the distance between A and B is simply the difference in the x-coordinates, which is not the case.