For Points P=(x_1,y_1) and Q(x_2,y_2) of the coordinate plane a new distance d(P,Q) is defined by d(P,Q) = |x_1 - x_2|+|y_1-y_2| Let O = (0,0) and A = (3,2). Prove that the set of points in the first quadrant which are equidistant (with respect to the new distance) from O and A consists of the union of a line segment of finite length and an infinite ray . Sketch this set in a labelled diagram. (10 marks)

- anonymous

- katieb

See more answers at brainly.com

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this

and **thousands** of other questions

- anonymous

The hardest part of this question is the language :/

- anonymous

I swear :P

- dumbcow

using the new distance definition, then for some point (x,y)
setting the distance equal to both O and A
\[\rightarrow |x| +|y| = |x-3| +|y-2|\]
now to show that is a union of line segment and ray ...

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

- dumbcow

hmm not a fan of absolute value functions

- anonymous

|x| + |y| = |x-3| + |y-2|
Since it's the first quadrant, x and y shall be positive.
x + y = |x-3| + |y-2|
Now up till (2,2)
The line should be x+y = -x + 3 - y + 2
2x + 2y = 5

- anonymous

Is this right?

- anonymous

yes. It is right. But I am facing the problem in understanding this question.

- anonymous

Hmm they (the question) have defined a new distance formula.

- anonymous

|dw:1335436017723:dw|And we are supposed to get the points which are equidistant from the points O and A, using the new distance formula. Is that right? @dumbcow

- dumbcow

correct

- anonymous

It should be the ditsnace individually. Suppose. See the dig below|dw:1335436193825:dw|
Like distance between O and P (by new distance formula) should be equal to distance between A and Q (by new distance formula)

- anonymous

*distance

- anonymous

I can't get the line after (3,2)
x + y = x-3 + y-2
Hmm are you sure the equation is correct? @shivam_bhalla

- anonymous

It is a question from IITJEE .

- dumbcow

it seems that no points outside (3,2) are equidistant to O and A

- anonymous

Hmm but the result can't lie. Maybe you could check the equation again? because the question says an infinite ray and finite distance, and we didn't get the infinite one.

- anonymous

The question is correct. I have referred from 2 books. It is a math question from IITJEE year 2000 (main)

- anonymous

Let me check.

- anonymous

See here. Question 4
->http://www.askiitians.com/iit-papers/IIT-JEE-2000-mathematics-mains.aspx

- anonymous

Strange the question is right
http://www.askiitians.com/iit-papers/IIT-JEE-2000-mathematics-mains.aspx

- anonymous

I have the 30 years, I will be back in a moment.

- dumbcow

http://www.wolframalpha.com/input/?i=abs%28x%29%2Babs%28y%29+%3D+abs%28x-3%29%2Babs%28y-2%29
looks like we forgot the case where y>2 but x<3
--> x = 1/2

- anonymous

ohh yeah

- anonymous

:-/ and I was trying to blame the question

- anonymous

lol, with enough practice you won't need wolfram. goodluck. :-)

- anonymous

Thanks :D

- anonymous

Study the 9 regions defined by the lines in the attacehd file, each one separtely.
It would be easy to get rid the absloute sign.
For eaxmple the bounded region we have
\[
0\le x \le 3\\
0\le y \le 2
\]
In this region we
3 - x + 2 -y = x + y
2 x + 2y = 5
y= -x + 5/2
Study the othe regions and see what you can get.

##### 1 Attachment

- anonymous

@eliassaab , Thanks for your help. I had initially problem in understanding the question. But I am comfortable with modulus function, just that my brain had gone blank at that time after reading the question :)

Looking for something else?

Not the answer you are looking for? Search for more explanations.