Question

derive the formula for the distance between two points x-2y+5 and x+2y+5​

Answer 1

0

Step-by-step explanation:

$The distance d between two parallel liens y=m x+c_{1} and y=m x+c_{2} is given by\\ d=\frac{\left|C_{1}-C_{2}\right|}{\sqrt{A^{2}+B^{2}}} \\ x-2 y+5 and x+2 y+5 \\Here A=1, B=-2, C_{1}=5 and C_{2}=5 \\ d=\frac{|5-5|}{\sqrt{1^{2}+(-2)^{2}}} \\ d=\frac{|0|}{\sqrt{1+4}} \\ d=\frac{0}{\sqrt{5}} \\ d=0$

To learn more

i) The distance between the pair of parallel lines represented by the expression x2 + 2xy + y2 - 8ax - 8ay - 9a2 = 0 is

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ii)How to find perpendicular distance of two given parallel lines?

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Answer 2

We correct the given problem by taking equations of straight lines:

• x - 2y + 5 = 0
• x + 2y + 5 = 0

First, we observe if the lines intersect each other:

The given straight lines are

x - 2y + 5 = 0 ..... (1)

x + 2y + 5 = 0 ..... (2)

From (1), we get x = 2y - 5 and substituting in (2), we have

2y - 5 + 2y + 5 = 0

or, 4y = 0

or, y = 0

Putting y = 0 in (1), we have x = - 5.

∴ the given lines intersect each other at (- 5, 0).

∴ being intersecting lines, the distance between the lines is 0.

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