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Find the perpendicular distance between the two parallel lines y = 4x + 5 and y = 4x + 7.
- a)1/√17 units
- b)2/√17 units
- c)3/√17 units
- d)4/√17 units
- e)5/√17 units
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Find the perpendicular distance between the two parallel lines y = 4x ...
To find the perpendicular distance between two parallel lines, we can use the formula:
Perpendicular distance = |b2 - b1| / √(m1^2 + 1)
where (m1, b1) and (m2, b2) are the slopes and y-intercepts of the two lines, respectively.
In this case, the two parallel lines are y = 4x + 5 and y = 4x + 7.
Comparing the equations, we can see that the slopes (m1 and m2) are both equal to 4, and the y-intercepts (b1 and b2) are 5 and 7, respectively.
Using the formula, we can calculate the perpendicular distance:
Perpendicular distance = |7 - 5| / √(4^2 + 1) Perpendicular distance = 2 / √(16 + 1) Perpendicular distance = 2 / √17
Simplifying further:
Perpendicular distance = 2 / √17 * (√17 / √17) Perpendicular distance = 2√17 / 17
Therefore, the perpendicular distance between the two parallel lines is 2/√17 units.
Hence, the correct answer is B: 2/√17 units.
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