P.S Coordinate Geometry

[divyalr]

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?

[fibo]

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

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

Then, if the legnth of the hipotenuse is 30. It´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.

[briantime]

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

[briantime]

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

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

[divyalr]

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?

[life is a test]

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.

[gmatv09]

slope (by defn) = AC/BC (rise over run)
4/3 = AC/BC
AC = (4/3)BC

Also, AB^2 = BC^2 + AC^2
AB = 30
Solve for BC ...

BC = 18