Distance Between a Point and a Line
Grade 10 Math worksheet on calculating the distance between a point and a line in a coordinate plane.
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Standards
Distance Between a Point and a Line
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Read each question carefully and show all your work. Use the provided coordinate planes for graphing when necessary.
1. In your own words, explain what the 'distance between a point and a line' means geometrically.
2. The formula for the distance between a point (x₁, y₁) and a line Ax + By + C = 0 is d = .
3. Calculate the distance between the point (3, -2) and the line 4x + 3y - 5 = 0.
4. On the coordinate plane below, plot the point P(-1, 4) and graph the line y = 2x + 1. Then, calculate the distance between point P and the line.
5. The shortest distance from a point to a line is always along the perpendicular segment from the point to the line.
True
False
Match each term with its definition.
a. Perpendicular line
1. A line that forms a 90-degree angle with another line.
b. Slope-intercept form
2. y = mx + b
c. Standard form
3. Ax + By + C = 0
6. Find the equation of the line that passes through the point (1, 5) and is perpendicular to the line 3x - y + 2 = 0. Then, calculate the distance between the point (1, 5) and the given line.