Use Coupon: CART20 and get 20% off on all online Study Material

Total Price: R

There are no items in this cart.
Continue Shopping
Get instant 20% OFF on Online Material.
coupon code: MOB20 | View Course list

Get extra R 350 off

Examples on Distance between two Parallel Lines


1.     Actually

                        d = + ax1+by1+c/√a2+b2

2.     To find the distance of a point from the given line, in the left side of the equation (right side being zero) substitute the co-ordinates of the point, and divide the result by √(coefficient of x)2 + (coefficient of y)2

3.     When to use complete perpendicular Distance formula? The complete perpendicular Distance formula is used when the length of the perpendicular to the line is given.



Find the distance of the point P(–2, 3) from the line AB which is 
x – y = 5.


The equation of the line is

        x – y – 5 = 0 [Making right side zero (note this step)]

 Perpendicular Distance of the point (2, 3)

        = (–2)–3–5/√(1)2+(–1)2 = –10/√2

        = –5√2

 Changing the sign, perpendicular Distance in magnitude = 5√2.

Enquiry:    We can now find the distance of a point form a line but how can we determine as to which side of the line does the point lie?

        From the figure, we observe that

                ax0 + by0 + c = 0     (? point (x0, y0) lies on the line)        …… (1)

30_Examples between two parallel lines 1.JPG

        Consider, ax1 + by1 + c

                = (ax0 + c) + by1                [x0 = x1 = x2]

                = b(y1 – y0)

                = –ve

        Consider, ax2 + by2 + c

                = (ax0 + c) + by2

                = b(y2 – y0)

                = +ve

Thus we observe that the point is on one side of the line, if put in the expression of line is gives one sign, while the point is on the other side of the line, if put in the expression of line it gives opposite sign.



Final the condition so that the points (x1, y1) and (x2, y2) lie on the same side, of the line ax + by + c =


Since, (ax1 + by1 + c) and (ax2 + by2 + c)

Should be of the same sign.

 Their product should be positive i.e.

        (ax1+by1+c)(ax2+by2+c) > 0, which is the required condition.

IIT JEE and AIEEE Mathematiics study material is available online free of cost at Study Physics, Chemistry and Mathematics at askIITians website and be a winner. We offer numerous live online classroom courses as well for live online IIT JEE preparation – you do not need to travel anywhere any longer – just sit at your home and study for IIT JEE live online with

To read more, Buy study materials of Straight Lines comprising study notes, revision notes, video lectures, previous year solved questions etc. Also browse for more study materials on Mathematics here.

  • Complete JEE Main/Advanced Course and Test Series
  • OFFERED PRICE: R 15,000
  • View Details
Get extra R 3,750 off