kelly116
kelly116 23h ago • 0 views

Test questions for distance from a point to a line with solutions

Hey there! 👋 Ever struggled with finding the distance from a point to a line? Don't worry, I've got you covered! This study guide and quiz will help you master this topic in no time. Let's dive in! 🧮
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steven.herrera Jan 5, 2026

📚 Quick Study Guide

  • 📐 The distance from a point $(x_0, y_0)$ to a line $Ax + By + C = 0$ is given by the formula: $d = \frac{|Ax_0 + By_0 + C|}{\sqrt{A^2 + B^2}}$.
  • 💡 Make sure the equation of the line is in the general form $Ax + By + C = 0$.
  • 📝 $(x_0, y_0)$ represents the coordinates of the point.
  • ➕ $A$, $B$, and $C$ are the coefficients from the line's equation.
  • ➗ Remember to take the absolute value of the numerator to ensure the distance is positive.

Practice Quiz

  1. Question 1: What is the distance from the point (1, 2) to the line $3x + 4y - 5 = 0$?
    1. A) 2
    2. B) 3
    3. C) 1
    4. D) 4
  2. Question 2: Find the distance from the point (-1, 1) to the line $x - y + 2 = 0$.
    1. A) $\sqrt{2}$
    2. B) $2\sqrt{2}$
    3. C) $\frac{\sqrt{2}}{2}$
    4. D) $\frac{3\sqrt{2}}{2}$
  3. Question 3: What is the distance from the origin (0, 0) to the line $5x - 12y + 26 = 0$?
    1. A) 1
    2. B) 2
    3. C) 3
    4. D) 4
  4. Question 4: Determine the distance from the point (2, -3) to the line $4x - 3y + 10 = 0$.
    1. A) 5
    2. B) 6
    3. C) 7
    4. D) 8
  5. Question 5: Calculate the distance from the point (4, 5) to the line $y = 2x + 3$.
    1. A) $\frac{2\sqrt{5}}{5}$
    2. B) $\frac{3\sqrt{5}}{5}$
    3. C) $\frac{\sqrt{5}}{5}$
    4. D) $\sqrt{5}$
  6. Question 6: What is the distance from the point (-2, -2) to the line $x + y = 0$?
    1. A) $\sqrt{2}$
    2. B) $2\sqrt{2}$
    3. C) $3\sqrt{2}$
    4. D) $\frac{\sqrt{2}}{2}$
  7. Question 7: Find the distance from the point (3, -1) to the line $x = 5$.
    1. A) 1
    2. B) 2
    3. C) 3
    4. D) 4
Click to see Answers
  1. Question 1: B) 3
  2. Question 2: B) $2\sqrt{2}$
  3. Question 3: B) 2
  4. Question 4: A) 5
  5. Question 5: B) $\frac{3\sqrt{5}}{5}$
  6. Question 6: B) $2\sqrt{2}$
  7. Question 7: B) 2

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