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

📚 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