Pythagorean Theorem and Distance between 2 points worksheet | Live ... - Free Printable

I'll solve this problem by finding the distance between each pair of points using the Pythagorean Theorem. The Pythagorean Theorem states that for a right triangle with legs of length $a$ and $b$, and hypotenuse of length $c$, we have $a^2 + b^2 = c^2$. In coordinate geometry, if we have two points $(x_1, y_1)$ and $(x_2, y_2)$, the distance between them is $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.

Let me go through each problem one by one.

Problem 1

First, I need to identify the coordinates of the two points.
- Top point: (-2, 5)
- Bottom point: (-2, -5)

Since these points have the same x-coordinate, the distance is simply the absolute difference in y-coordinates: $|5 - (-5)| = 10$.

Problem 2

Identifying the coordinates:
- Left point: (-2, -2)
- Right point: (4, 3)

Using the distance formula: $\sqrt{(4 - (-2))^2 + (3 - (-2))^2} = \sqrt{6^2 + 5^2} = \sqrt{36 + 25} = \sqrt{61}$.

Problem 3

Identifying the coordinates:
- Top point: (-1, 3)
- Bottom point: (-1, -3)

Since these points have the same x-coordinate, the distance is $|3 - (-3)| = 6$.

Problem 4

Identifying the coordinates:
- Left point: (0, -3)
- Right point: (3, -3)

Since these points have the same y-coordinate, the distance is $|3 - 0| = 3$.

Problem 5

Identifying the coordinates:
- Left point: (-3, -2)
- Right point: (0, 3)

Using the distance formula: $\sqrt{(0 - (-3))^2 + (3 - (-2))^2} = \sqrt{3^2 + 5^2} = \sqrt{9 + 25} = \sqrt{34}$.

Problem 6

Identifying the coordinates:
- Top point: (2, 3)
- Bottom point: (2, -3)

Since these points have the same x-coordinate, the distance is $|3 - (-3)| = 6$.

Problem 7

Identifying the coordinates:
- Left point: (2, 3)
- Right point: (5, 4)

Using the distance formula: $\sqrt{(5 - 2)^2 + (4 - 3)^2} = \sqrt{3^2 + 1^2} = \sqrt{9 + 1} = \sqrt{10}$.

Problem 8

Identifying the coordinates:
- Left point: (0, 1)
- Right point: (2, -1)

Using the distance formula: $\sqrt{(2 - 0)^2 + (-1 - 1)^2} = \sqrt{2^2 + (-2)^2} = \sqrt{4 + 4} = \sqrt{8} = 2\sqrt{2}$.

Now I'll summarize the answers:

1) Distance = 10
2) Distance = $\sqrt{61}$
3) Distance = 6
4) Distance = 3
5) Distance = $\sqrt{34}$
6) Distance = 6
7) Distance = $\sqrt{10}$
8) Distance = $2\sqrt{2}$