Question
If \( A \) and \( B \) have the coordinates \( (1,4) \) and \( (7,0) \) respectively, find the exact length of \( A B \). (2 marks) submit Answer
Ask by Burton Newton. in Singapore
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The exact length of \( AB \) is \( 2\sqrt{13} \) units.
Solution
To find the exact length of segment \( AB \) with coordinates \( A(1, 4) \) and \( B(7, 0) \), we can use the **distance formula**:
\[
AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
**Step-by-Step Calculation:**
1. **Substitute the coordinates into the formula:**
\[
AB = \sqrt{(7 - 1)^2 + (0 - 4)^2}
\]
2. **Calculate the differences:**
\[
AB = \sqrt{6^2 + (-4)^2}
\]
3. **Square the differences:**
\[
AB = \sqrt{36 + 16}
\]
4. **Sum the squares:**
\[
AB = \sqrt{52}
\]
5. **Simplify the square root:**
\[
AB = 2\sqrt{13}
\]
**Final Answer:**
The exact length of \( AB \) is \( 2\sqrt{13} \) units.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To find the exact length of the line segment \( AB \), you can use the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Here, the coordinates of point \( A \) are \( (1,4) \) and point \( B \) are \( (7,0) \). Plugging in the values: \[ d = \sqrt{(7 - 1)^2 + (0 - 4)^2} \] \[ = \sqrt{(6)^2 + (-4)^2} \] \[ = \sqrt{36 + 16} \] \[ = \sqrt{52} = 2\sqrt{13} \] The exact length of \( AB \) is \( 2\sqrt{13} \).
