Question
Find the distance between the lines with the equations
y = 3/2x+4 and −3x+2y = −1.
Round your answer to the nearest tenth.
y = 3/2x+4 and −3x+2y = −1.
Round your answer to the nearest tenth.
Answers
Reiny
y = 3/2x+4
2y = 3x + 8
3x - 2y + 8 = 0
-3x + 2y = -1
3x - 2y - 1 = 0 , so they are indeed parallel
pick any point on the first line,
e.g. let x = 2, then y = 7
so (2,7) lies on the first
distance from (2,7) to 3x - 2y - 1 = 0 is
|2(3) - 2(7) -1|/√(3^2 + (-2)^2)
= 9/√13
= appr 2.5
2y = 3x + 8
3x - 2y + 8 = 0
-3x + 2y = -1
3x - 2y - 1 = 0 , so they are indeed parallel
pick any point on the first line,
e.g. let x = 2, then y = 7
so (2,7) lies on the first
distance from (2,7) to 3x - 2y - 1 = 0 is
|2(3) - 2(7) -1|/√(3^2 + (-2)^2)
= 9/√13
= appr 2.5