Coordinate geometry

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Nycgrl: Master | Next Rank: 500 Posts; Posts: 124; Joined: Mon May 19, 2008 1:12 pm; Thanked: 3 times

by Nycgrl » Sat Oct 04, 2008 8:43 pm

In the xy-coordinate system, if (a, b) and (a + 3, b + k) are two points on the line defined by the equation x = 3y – 7, then k =
(A) 9
(B) 3
(C) 7/3
(D) 1
(E) 1/3

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Source: Beat The GMAT — Problem Solving | Sat Oct 04, 2008 8:43 pm

vishubn: Legendary Member; Posts: 574; Joined: Sun Jun 01, 2008 8:48 am; Location: Bangalore; Thanked: 28 times

by vishubn » Sat Oct 04, 2008 9:23 pm

Hi
K is 1

equation of the line we know
x = 3y – 7

3y=x+7
y=x/3+7/3----y=mx+c

when (a,b)= b=a/3+7/3
-->b=a+7/3

(a+3,b+k)=b+k=(a+3)/3+7/3
b+k=a+10/3
k=(a+10/3)-(a+7/3)
we get
k=(a+10-a-7)/3

where k=1

OA??

HTH
vishu

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aditi_bc: Senior | Next Rank: 100 Posts; Posts: 39; Joined: Wed May 14, 2008 11:41 am; Location: CA; Thanked: 2 times

by aditi_bc » Sat Oct 04, 2008 9:25 pm

Since both the points are on the line so they satisfy the line equation X=3Y-7
Substitute both the points(a,b) and (a+3,b+k) in the equation to form two separate equations and solve them to find the value of k.

So,by substituting (a,b) we get
a=3b-7 -----------(1)
And by substituting (a+3,b+k) we get,
a+3=3(b+k)-7 => a=3b+3k-10 -------(2)

Now sub value of 'a' from (1) in (2)

3b-7=3b+3k-10
solving we get 3k=3 => k=1

So answer is (D)

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Nycgrl: Master | Next Rank: 500 Posts; Posts: 124; Joined: Mon May 19, 2008 1:12 pm; Thanked: 3 times

by Nycgrl » Sat Oct 04, 2008 9:26 pm

Thanks ...OA is 1

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amitansu: Master | Next Rank: 500 Posts; Posts: 294; Joined: Tue Feb 26, 2008 9:05 pmFollowed by: 1 member; Thanked: 13 times

by amitansu » Sat Oct 04, 2008 9:36 pm

simplest way would be :

Given eq. x=3y-7=>y=x/3+7/3
so slope is 1/3

applying slopes formula => 1/3=b+k-b/a+3-a=>k=1

(slope=diff. of y coordinates/diff. x coordinates)

Amit

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