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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.

Grade 12 Math GeometryDistance Between a Point and a Line
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Includes

3 Short AnswerMultiple ChoiceFill in the BlanksTrue / False

Standards

CCSS.MATH.CONTENT.HSG.GPE.B.5CCSS.MATH.CONTENT.HSG.GPE.B.6

Topics

geometrydistance formulalinescoordinate geometrygrade 12
8 sections · Free to use · Printable
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Distance Between a Point and a Line

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Date:

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Read each question carefully and calculate the shortest distance between the given point and line. Show all your work.

1. Find the distance between the point (3, -2) and the line 4x + 3y - 6 = 0.

2. Calculate the distance between the point (-1, 5) and the line y = 2x + 3.

3. Which of the following is the correct formula for the distance between a point (x₀, y₀) and a line Ax + By + C = 0?

a

d = |Ax₀ + By₀ + C| / √(A² - B²)

b

d = |Ax₀ + By₀ + C| / √(A² + B²)

c

d = |Ax₀ - By₀ + C| / √(A² + B²)

d

d = |Ax₀ + By₀ - C| / √(A² + B²)

4. The shortest distance from a point to a line is along the   segment from the point to the line.

5. A line passes through the points (2, 1) and (6, 9). Find the distance between the origin (0, 0) and this line.

6. The distance between a point and a line is always a non-negative value.

T

True

F

False

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