Question

What is the total distance between (2, 12), (2, -4), and (-8, -4)?

Answer 1

To find the total distance between these three points, we can find the distance between each pair of points and then add them together.

The distance between two points (x1, y1) and (x2, y2) in a plane can be calculated using the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)

In this case, the three points are:
A: (2, 12)
B: (2, -4)
C: (-8, -4)

The distance between A and B is:
dAB = √((2 - 2)^2 + (-4 - 12)^2)
= √(0^2 + (-16)^2)
= √(0 + 256)
= √256
= 16

The distance between B and C is:
dBC = √((2 - (-8))^2 + (-4 - (-4))^2)
= √((2 + 8)^2 + (-4 + 4)^2)
= √(10^2 + 0^2)
= √(100 + 0)
= √100
= 10

The distance between A and C is:
dAC = √((2 - (-8))^2 + (12 - (-4))^2)
= √((2 + 8)^2 + (12 + 4)^2)
= √(10^2 + 16^2)
= √(100 + 256)
= √356

Now, we can add all the distances together to find the total distance:
Total distance = dAB + dBC + dAC
= 16 + 10 + √356

Hence, the total distance between the three points is 26 + √356, which is an irrational number.