P.S Coordinate Geometry

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

divyalr: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Wed Jul 23, 2008 6:28 am

P.S Coordinate Geometry

by divyalr » Tue Oct 13, 2009 9:32 pm

In the coordinate system above, line segments BC and AC are parallel to the x and y axes, respectively. If line segment AB has length 30 and is on a line that has slope 4/3, what is the length of BC?

(A) 28
(B) 24
(C) 21
(D) 18
(E) 15

Answer is D. How to solve the above?

Attachments

Quote

Source: Beat The GMAT — Problem Solving | Tue Oct 13, 2009 9:32 pm

fibo: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Mon Oct 19, 2009 12:39 pm

by fibo » Wed Oct 21, 2009 5:08 am

if slope is 4/3
when x=4
... y=3

Therefore hipotenuse is 5 (itÂ´s a 3,4,5 triangle).

Then, if the legnth of the hipotenuse is 30. ItÂ´s 6 times longer than our sample triangle (3,4,5). So the base of the triangle, will also be 6 times longer than in our sample (3*6=18).

Sample triangle: 3,4,5 (as length of different its sides).
Problem triangle: (3,4,5)*6 = 18, 24, 30.

Quote

briantime: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Sun Oct 18, 2009 3:39 am; Location: Baden-Baden, Germany; Thanked: 2 times; Followed by:1 members; GMAT Score:690

by briantime » Wed Oct 21, 2009 12:32 pm

Slope: 4/3

You can get the length ratios by just using random numbers if you are unsure:

x = 3:
f(x) = 4/3x + b (b doesn't matter here, so just dismiss it)
f(3) = (4/3)*3 = 4
Coords of B: (3,4)

x = 6:
f(6) = (4/3)*6 = 8
Coords of A: (6, 8)

Therefore:
Length of BC: 6-3 = 3
Length of AC: 8-4 = 4

We have a right triangle, there for the length ratios are 3:4:5.

Length AB = 30 = 6*5

Therefore:
Lenght BC = 3*6 = 18

Quote

briantime: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Sun Oct 18, 2009 3:39 am; Location: Baden-Baden, Germany; Thanked: 2 times; Followed by:1 members; GMAT Score:690

by briantime » Wed Oct 21, 2009 12:34 pm

fibo wrote:if slope is 4/3
when x=4
... y=3

if slope is 4/3:
when x = 3
then y = 4

Quote

divyalr: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Wed Jul 23, 2008 6:28 am

by divyalr » Thu Oct 22, 2009 11:16 am

briantime wrote:
fibo wrote:if slope is 4/3
when x=4
... y=3
if slope is 4/3:
when x = 3
then y = 4

How can you get the value of (x,y) from just the slope? Also..why do we leave the constant b?

Quote

life is a test: Master | Next Rank: 500 Posts; Posts: 138; Joined: Mon Mar 02, 2009 12:02 pm; Thanked: 15 times

by life is a test » Fri Oct 23, 2009 7:08 am

divyalr wrote:
briantime wrote:
fibo wrote:if slope is 4/3
when x=4
... y=3
if slope is 4/3:
when x = 3
then y = 4
How can you get the value of (x,y) from just the slope? Also..why do we leave the constant b?

the slope is the change in the y coords / change in x coords. 4/3 slope is saying that for every 4 units change in y, x will change 3 units. Hope the attached diag makes it easier to understand.

Attachments