Distance Between a Point and a Line
This worksheet focuses on calculating the distance between a given point and a line in a coordinate plane, including various forms of linear equations.
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Distance Between a Point and a Line
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Read each question carefully and show all your work. You may use a calculator for computations.
1. Find the distance between the point (3, 2) and the line y = 2x + 1.
2. Calculate the distance between the point (-1, 5) and the line 3x - 4y = 6.
3. Which formula is used to calculate the distance between a point (x₀, y₀) and a line Ax + By + C = 0?
d = |Ax₀ + By₀ + C| / sqrt(A² + B²)
d = |Ax₀ - By₀ - C| / sqrt(A² - B²)
d = sqrt((x₂ - x₁)² + (y₂ - y₁)²)
d = (y₂ - y₁) / (x₂ - x₁)
4. The distance between a point and a line is always a positive value.
True
False
5. A line passes through the points (1, 1) and (5, 3). Find the distance from the origin (0, 0) to this line.
6. To use the distance formula between a point and a line, the equation of the line must be in the form (Ax + By + C = 0).
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