Geometry
Parallel Line Through a Point Worksheets
Write the equation of a distinct parallel line through a given point, using slope-intercept, standard or mixed input equations.
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Perpendicular Line Through a Point Worksheets
Write perpendicular line equations through a given point, including exact fractional slopes and horizontal or vertical cases.
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Write each requested equation in slope-intercept form when possible; use x = c for a vertical line.
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Perpendicular lines have negative-reciprocal slopes. A horizontal line and a vertical line are perpendicular.
Learning objective
What this activity builds
Use negative reciprocal slopes or axis direction to find a perpendicular equation.
Worked example
Find the line perpendicular to y = 2x + 1 through (2, 3).
y = -1/2 x + 4.
The perpendicular slope is -1/2. Then 3 = (-1/2)(2) + b gives b = 4.
Teaching notes
Make the practice count
- Negate and invert a nonzero finite slope.
- A line perpendicular to a horizontal line is vertical.
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Eight equation tasks use exact integer or fractional slopes. Choose slope-intercept, standard, or mixed input forms.
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Related activities
Geometry
Parallel and Perpendicular Slopes Worksheets
Find both parallel and perpendicular slopes from integer or fractional slopes, with explicit zero and undefined slope practice.
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