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line or line segment

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line or line segment

by max37274 » Sat Apr 03, 2010 4:09 pm
In the rectangle coordinate system, triangle ABC has a vertex at point (0, 56). If point B is at the origin, then how many points on line AC have integer values for both their x and y values?

(1) The third vertex of triangle ABC lies on the x-axis, and the triangle has an area of 196

(2) Point A has a positive x coordinate and a y coordinate of zero

Guys this q has been discussed by the forum. My question is LINE AB extends in both directions NFINITELY and Line SEGMENT AB will give the anser A. UR COMMENTS PLS
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by thephoenix » Sat Apr 03, 2010 7:28 pm
from question we get two things
one vertex B is at origin and the other one (0,56) at y
now from s1) the third point is at x axis thus making the triangle a rt angled triangle
as the area of rt tri=1bh/2[where h=56 ar=196] we get the length of bASE and thus the x co ordinate of the 3rd vertex.
now it does not matters whether the thrd point is on 1st quard or sec quard;the information req will be same
hence A
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by eaakbari » Sat Apr 03, 2010 10:34 pm
IMO C

Statement one tells us a lot
Since one vertex on x axis, we can apply triangle area formula

1/2 * p * 56 = 196

which gives us p

But we do not know whether this p is point A or point C. Hence Insuff

Statement two.
Only tells us about points . Hence Insuff

Combined
From 1 we needed to know where the vertices were to have complete info, which statement two gives us

Hence C
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by kstv » Sun Apr 04, 2010 3:25 am
@ max37274 are u refering to this post if not have a look

https://www.beatthegmat.com/mba/2009/10/ ... cy-example

Since the area of the right angle triangle is 196 and height is 56 the third line is the base and the length is 7. The third point lies on the x axis and may have the value (7,0) or (-7,0)
the option (2) Point A has a positive x coordinate and a y coordinate of zero clears the doubt that the point is (7,0) and you are tempted to choose option C. In under 2 mins I will.
But if you draw the triangle you realise either way the hypotenuse AC will have only 6 integer values the exact no is not imp.
This is a very good question.
Attachments
integer values.jpg
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by max37274 » Sun Apr 04, 2010 7:59 pm
GUYS THANKS BUT YOU ARE NOT GETTING MY QUESTION. I HAVE NO CONFUSION AS TO HOW TO SOLVE IT.


HAD THE QUESTION STEM ASKED HOW MANY POINTS ARE INTEGERS ON LINE SEGMENT AB I M FINE WITH THE SOLUTION

BUT SINCE THE QUESTION IS HOW MANY POINTS ARE ON LINE AB (line ab BY DEFINITION EXTENDS INFINITELY IN BOTH DIRECTION I DONOT AGREE WITH THE ANSER AS THERE ARE INFINITE NUMBER OF INTEGER POSSIBLE
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by eaakbari » Sun Apr 04, 2010 8:59 pm
max37274 wrote:GUYS THANKS BUT YOU ARE NOT GETTING MY QUESTION. I HAVE NO CONFUSION AS TO HOW TO SOLVE IT.


HAD THE QUESTION STEM ASKED HOW MANY POINTS ARE INTEGERS ON LINE SEGMENT AB I M FINE WITH THE SOLUTION

BUT SINCE THE QUESTION IS HOW MANY POINTS ARE ON LINE AC (line ab BY DEFINITION EXTENDS INFINITELY IN BOTH DIRECTION I DONOT AGREE WITH THE ANSER AS THERE ARE INFINITE NUMBER OF INTEGER POSSIBLE

It does not extend infinitely in both direction. We are not given sufficient information as to whether C lies on negative or positive axis. How can a infinite entity have an area of 196?
Since its either positive axis or negative axis but both are symmetrical and will have same number of integer values. It thus answers question

Hth[/b]
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by max37274 » Mon Apr 05, 2010 7:01 am
ok. Again A Triangle consists of THREE LINE SEGMENTS AND NOT THREE LINES.

LINE SEGMENT AB IS FINITE BUT LINE AB NOT. TWO POINTS AB CAN BE USED TO FORM LINE SEGMENTS BUT ALSO LINES
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by max37274 » Mon Apr 05, 2010 7:03 am
EXPERTS PLS HELP OVER THE TERMINOLOGY USED
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by istuti » Tue Apr 06, 2010 3:26 am
Hi there,

When we talk about a line with definate end points such as line AB, it implicitly denotes a line segment.

When we talk about a line A with eqn y=mx+c then it extends till infinity.

Hope this clarifies.

Its quite late but still i thought of replying.

Thanks,
Istuti
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by istuti » Tue Apr 06, 2010 3:27 am
Hi there,

When we talk about a line with definate end points such as line AB, it implicitly denotes a line segment.

When we talk about a line A with eqn y=mx+c then it extends till infinity.

Hope this clarifies.

Its quite late but still i thought of replying.

Thanks,
Istuti
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