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
(sqaure root) 24 units
(square root) 50 units
(square root) 74 units
square root) 98 units
Answers
Answered by
GPT-4o mini
To find the distance between two points A and C using the Pythagorean Theorem, we need the lengths of the two legs of the right triangle formed by these points, which are represented as \(a\) and \(b\).
The Pythagorean Theorem states that:
\[
c = \sqrt{a^2 + b^2}
\]
Where \(c\) is the hypotenuse (the distance between the two points), and \(a\) and \(b\) are the lengths of the other two sides.
From your question, it appears that the options for distances are:
- \( \sqrt{24} \) units
- \( \sqrt{50} \) units
- \( \sqrt{74} \) units
- \( \sqrt{98} \) units
It seems you need to determine which of these values corresponds to the distance between points A and C using the Pythagorean Theorem. To do that, we need values for \(a\) and \(b\) in order to compute \(c\).
If you have these values, you can calculate \(c\) and then check which of the options represents that result. Without specific values for \(a\) and \(b\), we can't perform the calculation directly.
Suppose you have \(a^2 + b^2\) resulting in one of the square roots given, let’s proceed through the calculations for each option:
1. If \(c = \sqrt{24}\), then \(c^2 = 24\).
2. If \(c = \sqrt{50}\), then \(c^2 = 50\).
3. If \(c = \sqrt{74}\), then \(c^2 = 74\).
4. If \(c = \sqrt{98}\), then \(c^2 = 98\).
If you substitute \(a^2 + b^2\) into these, you can find which value matches.
Please provide the lengths \(a\) and \(b\) (or their squared values), and I can help determine which distance applies here!
The Pythagorean Theorem states that:
\[
c = \sqrt{a^2 + b^2}
\]
Where \(c\) is the hypotenuse (the distance between the two points), and \(a\) and \(b\) are the lengths of the other two sides.
From your question, it appears that the options for distances are:
- \( \sqrt{24} \) units
- \( \sqrt{50} \) units
- \( \sqrt{74} \) units
- \( \sqrt{98} \) units
It seems you need to determine which of these values corresponds to the distance between points A and C using the Pythagorean Theorem. To do that, we need values for \(a\) and \(b\) in order to compute \(c\).
If you have these values, you can calculate \(c\) and then check which of the options represents that result. Without specific values for \(a\) and \(b\), we can't perform the calculation directly.
Suppose you have \(a^2 + b^2\) resulting in one of the square roots given, let’s proceed through the calculations for each option:
1. If \(c = \sqrt{24}\), then \(c^2 = 24\).
2. If \(c = \sqrt{50}\), then \(c^2 = 50\).
3. If \(c = \sqrt{74}\), then \(c^2 = 74\).
4. If \(c = \sqrt{98}\), then \(c^2 = 98\).
If you substitute \(a^2 + b^2\) into these, you can find which value matches.
Please provide the lengths \(a\) and \(b\) (or their squared values), and I can help determine which distance applies here!
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