Question

. The distance of the point P (0, 0) from the line x + y + 1 = 0 measured parallel to the line y = 2x + 1 is
V5
15
(1)
(2)
2.
3
v2
(3)
(4)
3
3​

Answer 1

Answer:

d=√3389≈6.13 units

Step-by-step explanation:

Let equation of L1 be y=x−5, which has a slope m of 1.

and the equation of L3 be y=−2x−6

Now, draw a line from A(2,3) , parallel to L1, to meet L3 at P, as shown in the figure.

AP is the distance measured parallel to L1 from L3

Let the line joining A and P be L2.

Given that L2 is parallel to L1,

⇒L2 has the same slope (m=1) as that of L1,

Now find the equation of L2 through A(2,3) with a slope of m=1.

y=mx+b

⇒3=1×2+b,⇒b=1

⇒ the equation of L2 in slope-intercept form is y=x+1

Set the equations of L2andL3 equal to each other to find the intersection point P

⇒x+1=−2x−6,⇒x=−7/3

⇒y=−(7/3)+1=−4/3

⇒ coordinates of P=(−7/3,−4/3)

The distance from A(2,3) to P(−73,−43) is

d=√(−73−2)2+(−43−3)2

=√3389≈6.13 units