Question

find the distance of the line 4x - y=0 from the point (4,1) measured along the line making an angle of 135° with the positive x axis

Answer 1

Equation of line passing through the point (4,1) and making an angle of 135° with the positive x axis is given by:

y-a=m (x-b)→→General formula of equation of line passing through (a,b) and making an angle A with positive direction of x axis.where, m=tan A

So, equation of above line is

y-1=tan 135°(x-4)

y-1=-1(x-4)

y-1=-x +4

x+y=5

Now, we have to find the distance of line, 4 x-y=0 from the point (4,1).

The distance will be perpendicular distance which will be measured from line to point (4,1) $=\frac{4 \times 4-1}{\sqrt{4^2+1^2}}\\\\ =\frac{15}{\sqrt{17}}$

Given by the formula ,that is distance of line , ax + by + c=0 from point (p,q) is given by $=\frac{ap+bq+c}{\sqrt{a^2+b^2}}$

Answer 2

Answer:

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Step-by-step explanation:

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