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Pythagorean Theorem in Coordinate Systems
Question 1
Anna is trying to find the length of segment AC. Which equation could she use?
Responses
A AC = 2 + 7AC = 2 + 7
B
=
+
AC 2 = 4 2 + 1 2
C
=
+
AC 2 = 2 2 + 7 2
D
=
−
AC 2 = 7 2 − 2 2
Question 2
To the nearest tenth, which choice is the length of AC?
Responses
A 2.22.2
B 6.86.8
C 7.37.3
D 8.2
36:30
Skip to resourcesFeature
Pythagorean Theorem in Coordinate Systems
Question 1
Anna is trying to find the length of segment AC. Which equation could she use?
Responses
A AC = 2 + 7AC = 2 + 7
B
=
+
AC 2 = 4 2 + 1 2
C
=
+
AC 2 = 2 2 + 7 2
D
=
−
AC 2 = 7 2 − 2 2
Question 2
To the nearest tenth, which choice is the length of AC?
Responses
A 2.22.2
B 6.86.8
C 7.37.3
D 8.2
Answers
GPT-4o mini
To determine which response Anna could use for finding the length of segment AC, let's start by assuming segment AC connects points A and C in a coordinate plane. If we denote the coordinates of A as (x1, y1) and C as (x2, y2), the length of segment AC can be found using the Pythagorean theorem. The distance formula between two points in the coordinate system is given by:
\[
AC = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}
\]
If we rewrite this in terms of squares, we have:
\[
AC^2 = (x2 - x1)^2 + (y2 - y1)^2
\]
Now, let's analyze the given options for Question 1:
**Responses:**
- A: \( AC = 2 + 7 \) (Not applicable)
- B: \( AC^2 = 4^2 + 1^2 \) (This uses specific values which do not match our context without knowing A and C's coordinates.)
- C: \( AC^2 = 2^2 + 7^2 \) (This follows the distance formula of the Pythagorean theorem.)
- D: \( AC^2 = 7^2 - 2^2 \) (This is incorrect as the Pythagorean theorem adds the squares, not subtracts.)
Based on the analysis, the correct response for Question 1 is:
**C: \( AC^2 = 2^2 + 7^2 \)**
---
For Question 2, we need to calculate the length of AC using the equation from option C:
\[
AC^2 = 2^2 + 7^2
\]
Calculating these squares:
\[
AC^2 = 4 + 49 = 53
\]
To find AC, we take the square root:
\[
AC = \sqrt{53} \approx 7.28
\]
Rounding to the nearest tenth gives us 7.3. Therefore, the best response for Question 2 is:
**C: 7.3**
\[
AC = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}
\]
If we rewrite this in terms of squares, we have:
\[
AC^2 = (x2 - x1)^2 + (y2 - y1)^2
\]
Now, let's analyze the given options for Question 1:
**Responses:**
- A: \( AC = 2 + 7 \) (Not applicable)
- B: \( AC^2 = 4^2 + 1^2 \) (This uses specific values which do not match our context without knowing A and C's coordinates.)
- C: \( AC^2 = 2^2 + 7^2 \) (This follows the distance formula of the Pythagorean theorem.)
- D: \( AC^2 = 7^2 - 2^2 \) (This is incorrect as the Pythagorean theorem adds the squares, not subtracts.)
Based on the analysis, the correct response for Question 1 is:
**C: \( AC^2 = 2^2 + 7^2 \)**
---
For Question 2, we need to calculate the length of AC using the equation from option C:
\[
AC^2 = 2^2 + 7^2
\]
Calculating these squares:
\[
AC^2 = 4 + 49 = 53
\]
To find AC, we take the square root:
\[
AC = \sqrt{53} \approx 7.28
\]
Rounding to the nearest tenth gives us 7.3. Therefore, the best response for Question 2 is:
**C: 7.3**