Find the distance between the pair of parallel lines. y = 2x + 4, y = 2x - 3
2 answers:
Answer:
3.13
Step-by-step explanation:
Given :
y = 2x + 4 -------- eq1
y = 2x - 3 -------- eq2
sanity check : both equations have same slope, so we can conclude that they are both parallel to one another.
Step 1: consider equation 1, pick any random x-value and find they corresponding y-value. we pick x = -2
This gives us y = 2(-2) + 4 = 0
Hence we get a point (x,y) = (-2,0)
Step 2: express equation 2 in general form (i.e Ax + By + C = 0)
y = 2x-3 -------rearrange---> 2x - y -3 = 0
Comparing with the general form, we get A = 2, B = -1, C = -3
Recall that the distance between 2 parallel lines is given by the attached formula (see attached picture).
substituting the values for A, B, C and (x, y) from the previous step:
d = | (2)(-2) + (-1)(0) + (-3) | / √(2² + (-1)²)
d = | -4 + 0 - 3 | / √(4 + 1)
d = | -7 | / √5
d = 7 / √5
d = 3.13
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