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The distance between the lines 5x – 12y + 65 = 0 and 5x – 12y – 39 = 0
- a)2
- b)- 2
- c)8
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
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The distance between the lines 5x – 12y + 65 = 0 and 5x – ...
The equation of a line in standard form is Ax + By = C, where A, B, and C are constants.
The line 5x - 2y = 7 can be rewritten as -2y = -5x + 7 by isolating y.
Dividing both sides of the equation by -2, we get y = (5/2)x - 7/2.
The line 3x + 4y = 9 can be rewritten as 4y = -3x + 9 by isolating y.
Dividing both sides of the equation by 4, we get y = (-3/4)x + 9/4.
To find the distance between the lines, we can use the formula:
d = |(C1 - C2) / √(A^2 + B^2)|
where (C1, C2) are the constants in the equations of the lines, and A and B are the coefficients of x and y, respectively.
For the first line, A = 5, B = -2, and C1 = 7.
For the second line, A = 3, B = 4, and C2 = 9.
Substituting these values into the formula, we get:
d = |(7 - 9) / √(5^2 + (-2)^2)|
d = |-2 / √(25 + 4)|
d = |-2 / √29|
Therefore, the distance between the lines 5x - 2y = 7 and 3x + 4y = 9 is |-2 / √29|.
The line 5x - 2y = 7 can be rewritten as -2y = -5x + 7 by isolating y.
Dividing both sides of the equation by -2, we get y = (5/2)x - 7/2.
The line 3x + 4y = 9 can be rewritten as 4y = -3x + 9 by isolating y.
Dividing both sides of the equation by 4, we get y = (-3/4)x + 9/4.
To find the distance between the lines, we can use the formula:
d = |(C1 - C2) / √(A^2 + B^2)|
where (C1, C2) are the constants in the equations of the lines, and A and B are the coefficients of x and y, respectively.
For the first line, A = 5, B = -2, and C1 = 7.
For the second line, A = 3, B = 4, and C2 = 9.
Substituting these values into the formula, we get:
d = |(7 - 9) / √(5^2 + (-2)^2)|
d = |-2 / √(25 + 4)|
d = |-2 / √29|
Therefore, the distance between the lines 5x - 2y = 7 and 3x + 4y = 9 is |-2 / √29|.
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The distance between the lines 5x – 12y + 65 = 0 and 5x – 12y – 39 = 0a)2b)- 2c)8d)none of theseCorrect answer is option 'C'. Can you explain this answer?
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