Question

A straight line L is drawn through the point
A(2, 1) such that its point of intersection with
the straight line x + y = 9 is at a distance of
3√2 from A. Find the angle which the line L
makes with the positive direction of the x-axis.
plz chapava​

Answer 1

Step-by-step explanation:

Let the point of intersection be P(h,k)

As P is on x+y=9

⇒k=9−h

⇒P(h,9−h)

Given, PA=3

2

⇒

(h−2)

2

+(g−h−1)

2

=3

2

⇒(h−2)

2

+(h−8)

2

=18

⇒2h

2

−20h+50=0

⇒h

2

−10h+25=0

⇒(h−5)

2

=0

⇒h=5⇒k=4

⇒L passes through (5,4) and (2,1)

⇒ Slope =

5−2

4−1

=

3

3

=1

⇒tanθ=1

⇒θ=

4

π

.