Use the Pythagorean Theorem to find the distance between points A and D.

A 2sqrt(2)

B 2sqrt(3)

C 3sqrt(5)

D sqrt(34)

1 answer

To find the distance between points A and D, we first need to find the length of the line segment AD. Let's label the points: A(x1, y1) = (0, 0) and D(x2, y2) = (2, 4).

Now we can use the Pythagorean Theorem, which states: a^2 + b^2 = c^2, where c is the hypotenuse (in this case, the distance between A and D).

The length of the side adjacent to the x-axis (a) is the difference in x-coordinates:
a = x2 - x1 = 2 - 0 = 2.

The length of the side adjacent to the y-axis (b) is the difference in y-coordinates:
b = y2 - y1 = 4 - 0 = 4.

Now we can plug these values into the Pythagorean Theorem:
c^2 = 2^2 + 4^2
c^2 = 4 + 16
c^2 = 20

To find c, take the square root of both sides:
c = sqrt(20) = sqrt(4*5) = 2sqrt(5)

Therefore, the distance between points A and D is 2sqrt(5), which is not one of the answer choices provided.