Question:
The distance of the point $P(1,-3)$ from the line $2y - 3x = 4$ is:
The distance of the point $P(1,-3)$ from the line $2y - 3x = 4$ is:
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Always convert to standard form before applying formula.
Updated On: Apr 30, 2026
- \(\sqrt{13} \text{ units} \)
- \(13 \text{ units} \)
- \(7 \text{ units} \)
- \(\sqrt{7} \text{ units} \)
- \(2\sqrt{13} \text{ units} \)
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The Correct Option is A
Solution and Explanation
Concept:
Distance formula:
\[
d = \frac{|Ax_1 + By_1 + C|}{\sqrt{A^2 + B^2}}
\]
Step 1: Convert to standard form.
\[ -3x + 2y - 4 = 0 \]
Step 2: Substitute values.
\[ d = \frac{| -3(1) + 2(-3) - 4 |}{\sqrt{13}} = \frac{13}{\sqrt{13}} = \sqrt{13} \]
Step 1: Convert to standard form.
\[ -3x + 2y - 4 = 0 \]
Step 2: Substitute values.
\[ d = \frac{| -3(1) + 2(-3) - 4 |}{\sqrt{13}} = \frac{13}{\sqrt{13}} = \sqrt{13} \]
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