Parallel lines - dist
Find the distance between the parallel lines 3x – 4y +7 = 0 and 3x – 4y + 5 = 0
Correct answer:
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Dr. Math
The distance between two parallel lines in the plane can be computed using the following formula:
where A, B, and C are coefficients and L1 ∥ L2 (they have identical slopes).
The distance d between L1 and L2 is:
1. Ensure the lines are parallel by verifying that their coefficients A and B are identical (or proportional).
2. Put both lines in the same form (usually Ax + By + C = 0).
3. Apply the formula by plugging in C1 and C2.
Given Two Parallel Lines:
begin{align*}
L1 &: Ax + By + C1 = 0,
L2 &: Ax + By + C2 = 0,
end{align*}
L1 &: Ax + By + C1 = 0,
L2 &: Ax + By + C2 = 0,
end{align*}
where A, B, and C are coefficients and L1 ∥ L2 (they have identical slopes).
Distance Formula:
The distance d between L1 and L2 is:
d = |C2 - C1| √A2 + B2 .
Steps to Compute the Distance:
1. Ensure the lines are parallel by verifying that their coefficients A and B are identical (or proportional).
2. Put both lines in the same form (usually Ax + By + C = 0).
3. Apply the formula by plugging in C1 and C2.
Tips for related online calculators
The line slope calculator is helpful for basic calculations in analytic geometry. The coordinates of two points in the plane calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of the segment, intersections of the coordinate axes, etc.
Our vector sum calculator can add two vectors given by their magnitudes and by included angle.
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The Pythagorean theorem is the base for the right triangle calculator.
Our vector sum calculator can add two vectors given by their magnitudes and by included angle.
Do you want to convert length units?
The Pythagorean theorem is the base for the right triangle calculator.
You need to know the following knowledge to solve this word math problem:
- geometry
- analytic geometry
- line
- vector
- arithmetic
- square root
- absolute value
- planimetrics
- Pythagorean theorem
Units of physical quantities:
Grade of the word problem:
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