WEEK 3 graded Q5

[SUHANA PARVEEN S]

The equation of the straight road which is equidistant from two parallel straight roads represented by 6x+4y−5=0 and 3x+2y+4=0 is

12x−8y+3=0

8x−12y−3=0

12x+8y+3=0

8x+12y+3=0

No, the answer is incorrect.
Score: 0 Accepted Answers:

12x+8y+3=0

Can someone help me with this question. My findings are 8x + 12y + 3 = 0, even though I did it twice  

Regards

[Anand Iyer]

so, here's one observation that'll help.

Given two roads are parallel, and from the question, it's clear that the third road also must be parallel.

Thus, on a reduced form of all 3 equations, A and B must be equal.

The only option that works is the 3rd one - 12x + 8y + 3 = 0.

if you're confused on how to proceed please reply.

[Debajyoti Biswas]

Thanks, Anand for the correct answer

[SUHANA PARVEEN S]

Ys anand they are parallel. I have gone through it also. But getting ans as d. 

I solved using one another method.

Regards

On Tuesday, November 3, 2020 at 12:50:35 PM UTC+5:30 anandd...@gmail.com wrote:

[Malabika Guha Mustafi]

@ Suhana , would you please share your method if it is not a problem. I am interested to see it. 

[SUHANA PARVEEN S]

ok...fine I will

[Patil Sai Vaishnavi]

If a straight road is equidistant from 2 parallel roads then the eq of st road should be also parallel to both the roads right

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[SUHANA PARVEEN S]

Thats right...

[SUHANA PARVEEN S]

It's similar to what we have studied . Since they are are equidistant and parallel 

 

Solved using this..

Regards  

On Tuesday, November 3, 2020 at 1:38:35 PM UTC+5:30 Malabika Guha Mustafi wrote:

[Anand Iyer]

Ok, let's do this again.

We've 3 parallel lines

1.   6x+4y−5=0

2.  3x+2y+4=0  

3.  ??

We have to identify the 3rd one from the options.  That's our task.

General form of an equation is Ax +By + C = 0

All lines parallel to the general form of the equation (of al line) will be its multipliers, excepting the y-intercept (represented by C)

If you notice, the second equation is 2 times first.  Thus 2 * (3x+2y) = 6x+4y.  That's the reason these two lines are parallel. in the first place.  Of course, c must be excluded when you do this.

Also see, 4 * (3x + 2y) = 12x + 8y.  Hence the two lines 3x+2y+4=0  and 12x+8y+3=0 are parallel.

This is your 3rd option.

[SUHANA PARVEEN S]

Sorry Here is the attachment..!!!

[Malabika Guha Mustafi]

Ok, so you decided to take a point on the line and try to figure out the equation. Actually, my approach was the same . But considering a point of the line I took the the line itself.

so , the equation became ,C+5/2 = -(C-4)  [considering A=3, B=2, since they are parallel so reduced 6x + 4y -5 to 3x+2y -5/2 as explained by Anand,]..

The main problem with your approach is considering point [ formula is the distance between a point and the line not between two lines] instead of line.

Please remind that, a point  may be equidistant  from two given line but it is not ensured that line passing through the point is also equidistant from that two lines.

[SUHANA PARVEEN S]

Thanks to all..A special thanks to Malabika..

I have understood my mistake!!

Regards

Suhana

[Malabika Guha Mustafi]

Welcome