Question

Apply the Pythagorean Theorem to find the distance between points A and C.
(sqaure root) 24 units
(square root) 50 units
(square root) 74 units
square root) 98 units

It's a graph
C is at the top and then B is also at the top but 7 spots away and a in in the middle of the graph 5 spots down from A

Answer 1

To find the distance between points A and C using the Pythagorean Theorem, we first need more specific coordinates for points A, B, and C. However, based on your description, we can take it step by step to identify how to apply the theorem.

1. **Understanding Coordinates:**
- If we place point C at (0, 0), then point B, which is directly above C at (0, 7) (since it is 7 units up), will have coordinates (0, 7).
- Point A is said to be in the middle and 5 units down from B. Therefore, if B is at (0, 7), then A is at (0, 7 - 5) = (0, 2).

2. **Setting Coordinates:**
- Let’s summarize our points:
- \( C(0, 0) \)
- \( B(0, 7) \)
- \( A(0, 2) \)

3. **Finding Distance:**
- Now, we need to find the distance between points A and C.
- According to the Pythagorean Theorem, the distance \( d \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
- For points A(0, 2) and C(0, 0), we can substitute the coordinates:
\[
d = \sqrt{(0 - 0)^2 + (0 - 2)^2} = \sqrt{0 + 4} = \sqrt{4} = 2
\]

Based on the details you've provided, the distance between points A and C is 2 units, which doesn’t seem to match with the distances you initially provided (24, 50, 74, or 98). If the diagram or coordinates are different than understood, please clarify, and I can help you calculate the correct distance.