M21-33

Question

What is the area of the triangle formed by lines  y = 5-x ,  2y = 3x , and  y = 0 ?

A. 7.5
B. 8.0
C. 9.0
D. 10.5
E. 15.0

chetan2u · Accepted Answer

Hi,
you have three equations which are equqtion of line..
when you solve for x and y between any two of them, these value of x and y will give you intersection of the two lines, which would be same as the vertices..
you will hAVE three sets of two equations so three vertices..
just an example
 y=5−x, 2y=3x, and y=0..

say y=5-x and y=0..
here x=5 and y=0.. this is one of the vertices

similarly 2y=3x and y=0..
here x=0 and y=0..

and the third can be found from 
y=5−x, 2y=3x
hope it is clear

Bunuel · Answer

Official Solution:

What is the area of the triangle formed by lines  y = 5-x ,  2y = 3x , and  y = 0 ?

A. 7.5
B. 8.0
C. 9.0
D. 10.5
E. 15.0

Look at the diagram below:
 
 https://gmatclub.com/gmat-practice-tests/resources/import/img/m21-33.png 
 
The vertices of the triangle are  (0, 0) ,  (5, 0)  and  (2, 3) . So,  Base=5 ,  Height=3  and  Area=\frac{1}{2}*Base*Height=7.5 .

Answer: A

vik09 · Answer

Hello,
Can you please tell that how you got the vertices of the triangle from the given equations.

Regards & Thanks

vik09 · Answer

Hello,
Thanks a lot for your reply. I want to ask one thing that every time when we will solve for x and y from two equations the values that we get for x and y will be the intersection of two points ??. The other point is clear that they will act as vertices.

Sorry if my question is lame ... actually I struggle a lot in Co-Geo apart from P&C.

chetan2u · Answer

Hi,
look what does each equation of line tells us ..
 it has two coord x and y , and by taking different values of x and y that fit into that equation and putting them into the graph we have a line.. 
So when we have two such lines ,  we will have two sets of values of x and y with only one set of values of x and y common to two sets and that is the point where these two lines intersect...  of course we will have no set of value common incase of parallel lines and their slope will be same 
hope it was helpful

vik09 · Answer

Thanks <img src="{SMILIES_PATH}/icon_smile.gif" alt=":)" title="Smile" />

Senthil7 · Answer

I think this is a  high-quality  question and I agree with explanation.

mbadude2017 · Answer

A 30 second shortcut is to find the determinant of a matrix and halve it. So...

|1 1 5|
|-3 2 0|
|0 1 0|

gives 1*(2*0-1*0) - 1*(-3*0-0*0) + 5*(-3*1--2*0) = -15
area is abs(-15)/2 = 15/2

spetznaz · Answer

+1 for A. Draw a graph an get the answer. The area of the triangle is (1/2)*(b)*(h). The sides are x-axis, line x+y=5 and y=(3/2)x. The base is 5 units and height is 3. The area is 15/2 or 7.5 units. The answer is hence option A.

pinguuu · Answer

Can you please explain the shortcut please? thanks

mangamma · Answer

Take each value x, y, constant and form a matrix and divide by 2

SpecterLitt · Answer

Hey!

I struggle in Coordinate Geometry. 
So, my question might be dumb.

Aren't there 2 triangles being formed in the figure. The area of once is coming as 7.5 & the other's 5. How do I decide which one to pick

Bunuel · Answer

Check the image below: https://gmatclub.com/forum/download/file.php?id=54529 Three lines y = 5-x (blue line), 2y = 3x (green line), and y = 0 (red line) form only one triangle. Untitled.png

davidbeckham · Answer

Hi  Bunuel , coordinate geometry is my weak area, I didn't understand how did you derive the coordinates from the equations - could you please explain?

Bunuel · Answer

24. Coordinate Geometry 
     Theory   
 Math: Coordinate Geometry 
 Beauty of Coordinate geometry 
 Dealing with Tangents on the GMAT 
     Questions   
 DS Questions 
 PS Questions

For more check:
 ALL YOU NEED FOR QUANT ! ! ! 
 Ultimate GMAT Quantitative Megathread

Hope it helps.

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