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Coordinate Geomatry

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Coordinate Geomatry

by richs_ca » Fri May 02, 2008 11:15 am
In the XY-coordinate plane, the slope of line l is 3/4. Does line l pass through the point (-2/3, 1/2)?

1) Line l passes through the point (4,4)

2) Line l passes through the the point (-4, -2)

I know that the answer is C because there is sufficient information to figure out the entire line. I just have no idea how to solve these kinds of problems.

Help!
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by simplyjat » Fri May 02, 2008 11:18 am
The answer is not C, but the answer is D. Pay close attention on the slope mentioned in the stem. If we have slope of a line and one point on the line we can uniquely identify the line...
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by richs_ca » Fri May 02, 2008 11:31 am
THanks, Simplyjat.

I'm still trying to figure out how to work with these problems, and with the equation y=mx+b.

Am i correct to just plug in one of those coordianates into the equation and then solve for b?
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by simplyjat » Fri May 02, 2008 11:35 am
richs_ca wrote: Am i correct to just plug in one of those coordianates into the equation and then solve for b?
Yeah you are correct when you plug in the values of x, y and m in y = mx + c to get the value of c, and thus finding out the whole equation. But the question is a data sufficiency problem and you need not to solve the equation; you just need to know what you need in order to solve the equation.
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by II » Fri May 02, 2008 2:38 pm
To add to SimplyJat's comments.

With this question, the first thing you should do is write down the equation of a line formula:
y = mx + c (where m is the slope/gradient, and c is the y-intercept)

We already know the slope ... this is 3/4. so m = 3/4.
We can now write the equation as:
y = (3/4)x + c

So in the question stem we are given a co-ordinate, in both statements we are given co-ordinates. These coordinates are values for x and y. So if we have these values for x, y, and m, then we can easily find the value for c, and subsequently have enough (SUFFICIENT) information to answer the question.

As simplyjat pointed out ... you dont have to go through the full calculation to find the actual answer ... just need to know that you have all the information you need to do so ... sufficent data ! This is KEY for DS questions, and will save you so much time.

Hope this makes sense.
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by netigen » Fri May 02, 2008 2:45 pm
For this Q, you do not even need to find the equation of the line.

Just use the slope formula m = (y1-y2)/(x1-x2)

We already have x1,y1 in the question stem

A and B both give us x2,y2 so each is SUFF

Ans is D
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by llewellyn27 » Thu Jun 05, 2008 12:36 pm
Netigen

I did it the same way

M = Y2-Y1 / X2-X1

Macth up the answer that you get with slope given in the stem.

If they match then the line passes thru the point. If not then it does not pass thru
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by chetanojha » Sun Mar 29, 2009 5:28 am
Slope of Line=3/4. Hence Equation of line y=(3/4)x+b
Since the line pass through the point (-2/3,1/2) we can use these coordinates to find the y- intercepts i.e. b in the above equation

Substitute (-2/3,1/2) in y=(3/4)x+b

1/2=(3/4)(-2/3)+b ==>b=1

Putting b back into equation y=(3/4)x+b gives y=(3/4)x+1

Now since we want to find that line pass through different points.

1. point (4,4). Put the x coordinate in equation y=(3/4)x+1 and check if y=4. If y=4 then line pass through the point.
SUFFICIENT
2.point (-4,-2). Put the x coordinate in equation y=(3/4)x+1 and check if y=-2. If y=-2 then line pass through the point.
SUFFICIENT

ANSWER: D
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by chetanojha » Sun Mar 29, 2009 5:28 am
Slope of Line=3/4. Hence Equation of line y=(3/4)x+b
Since the line pass through the point (-2/3,1/2) we can use these coordinates to find the y- intercepts i.e. b in the above equation

Substitute (-2/3,1/2) in y=(3/4)x+b

1/2=(3/4)(-2/3)+b ==>b=1

Putting b back into equation y=(3/4)x+b gives y=(3/4)x+1

Now since we want to find that line pass through different points.

1. point (4,4). Put the x coordinate in equation y=(3/4)x+1 and check if y=4. If y=4 then line pass through the point.
SUFFICIENT
2.point (-4,-2). Put the x coordinate in equation y=(3/4)x+1 and check if y=-2. If y=-2 then line pass through the point.
SUFFICIENT

ANSWER: D
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by bhumika.k.shah » Tue Feb 02, 2010 7:54 am
Hey could anyone suggest any good books/links for getting my basics cleared in co-ordinate geometry ??

i am quite weak in that topic :-(
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by ajith » Tue Feb 02, 2010 8:33 am
bhumika.k.shah wrote:Hey could anyone suggest any good books/links for getting my basics cleared in co-ordinate geometry ??

i am quite weak in that topic :-(
https://www.mathopenref.com/coordintro.html

I like this
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by Mom4MBA » Tue Feb 02, 2010 1:06 pm
Answer is D

instead of using y=mx+c I used y-y1 = m(x-x1)

Given point (-2/3,1/2) and slope m=3/4

take statement 1:
given point is (4,4)

y-4=3/4 (x-4)

now put point (-2/3,1/2) if it satisfies the equation it lies on the line else not.

now take statement 2:
given point is (-4,-2)

y+2=3/4 (x+4)

now put point (-2/3,1/2) if it satisfies the equation, it lies on the line else not.

So each statement alone is enough.
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by harsh.champ » Wed Feb 03, 2010 12:58 am
Mom4MBA wrote:Answer is D

instead of using y=mx+c I used y-y1 = m(x-x1)

Given point (-2/3,1/2) and slope m=3/4

take statement 1:
given point is (4,4)

y-4=3/4 (x-4)

now put point (-2/3,1/2) if it satisfies the equation it lies on the line else not.

now take statement 2:
given point is (-4,-2)

y+2=3/4 (x+4)

now put point (-2/3,1/2) if it satisfies the equation, it lies on the line else not.

So each statement alone is enough.

_______________________
I do agree with the solution,though these can also be arrived at using the equation:y=mx + c.
After all,(y1-mx1)=c if you carefully analyse the equation.
The basic concept to be kept in mind is that (1)slope and (2)a point on the line is required to extract the equation of a unique line.
Hence,both the statements alone are enough to answer the question. :)
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by Mom4MBA » Wed Feb 03, 2010 5:30 am
Thanks harsh.champ, I know this approach too, it was just that I was giving one more way to solve it because nobody had mentioned it.
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by venmic » Sat Jun 18, 2011 2:51 pm
I like this approach better
the other does NOT seem correct

because the question if it passes through a point you cannot use that to find a value

Mom4MBA wrote:Answer is D

instead of using y=mx+c I used y-y1 = m(x-x1)

Given point (-2/3,1/2) and slope m=3/4

take statement 1:
given point is (4,4)

y-4=3/4 (x-4)

now put point (-2/3,1/2) if it satisfies the equation it lies on the line else not.

now take statement 2:
given point is (-4,-2)

y+2=3/4 (x+4)

now put point (-2/3,1/2) if it satisfies the equation, it lies on the line else not.

So each statement alone is enough.
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