Question

Line ℓ1 has the equation

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x+y=
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5 and line ℓ2 has the equation
-
x+y=
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3. Find the distance between ℓ1 and ℓ2.

Answer 1

`√(2)` units

Explanation:

The Line 1 has equation x + y = 5 ....... (1) , and

Line 2 has equation x + y = 3 .......... (2)

Now, we have to find the perpendicular distance between line 1 and line 2.

We can say that (3,0) is a point on line 2 as it satisfies the equation (2).

Now, the perpendicular distance from point (3,0) to the line 1 will be given by the formula

`\frac{\sqrt{1^(2)+ 1^(2)}} = (2)/(√(2)) = √(2)` units (Answer)

We know that the perpendicular distance from any external point (
`x_(1),y_(1)`) to a given straight line ax + by + c = 0 is given by the formula
`\frac{\sqrt{a^(2) + b^(2)}}`.