Question

Line ℓ1 has the equation

Answer 1

Answer:

$\sqrt{2}$ units

Step-by-step 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

$\frac{|3 + 0 - 5|}{\sqrt{1^{2}+ 1^{2}}} = \frac{2}{\sqrt{2}} = \sqrt{2}$ 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 $\frac{|ax_{1} + by_{1} + c|}{\sqrt{a^{2} + b^{2}}}$.