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, covering 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 calculate the distance between the given point and line. Show all your work.
1. Find the distance between the point (2, 3) and the line 3x + 4y - 6 = 0.
2. Calculate the distance between the point (-1, 5) and the line y = 2x + 1.
3. Determine the distance between the point (0, 0) and the line x - y + 7 = 0.
1. The formula for the distance between a point (x₁, y₁) and a line Ax + By + C = 0 is .
2. If a line is in the form y = mx + c, it needs to be converted to the form before applying the distance formula.
3. The shortest distance from a point to a line is always along a segment to the line.
1. The distance from a point to a line can never be negative.
True
False
2. If a point lies on the line, the distance between the point and the line is 1.
True
False
1. Which of the following lines is parallel to the line 2x - y + 5 = 0?
y = -2x + 3
y = 2x - 1
y = (1/2)x + 4
y = -(1/2)x - 2
2. What is the perpendicular distance from the origin (0,0) to the line 4x - 3y = 10?
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1. Plot the point P(1, -2) and the line 2x + y = 4 on the coordinate plane below. Then, visually estimate and calculate the distance between them.
Calculated Distance: