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In the XY-plane, what is the area of the triangle formed by the line 3

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In the XY-plane, what is the area of the triangle formed by the line 3  [#permalink]

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11 Jul 2017, 02:34
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In the XY-plane, what is the area of the triangle formed by the line 3y − 4x = 24 and the X and Y axes?

(A) 6
(B) 14
(C) 24
(D) 36
(E) 48

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Re: In the XY-plane, what is the area of the triangle formed by the line 3  [#permalink]

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11 Jul 2017, 02:44
Bunuel wrote:
In the XY-plane, what is the area of the triangle formed by the line 3y − 4x = 24 and the X and Y axes?

(A) 6
(B) 14
(C) 24
(D) 36
(E) 48

Line $$3y-4x=24$$ intersects $$Ox$$ at $$A(-6, 0)$$
Line $$3y-4x=24$$ intersects $$Oy$$ at $$B(0, 8)$$

Hence, the area of the triangle OAB is $$\frac{6*8}{2}=24$$

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Re: In the XY-plane, what is the area of the triangle formed by the line 3  [#permalink]

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14 Jul 2017, 09:08
3y=4x+24
(x,y) can have values - (-6,0),(-3,4),(0,8)

when this is traced on graph --> The triangle is formed with Base - 6 and Height - 8
1/2*6*8= 24

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Re: In the XY-plane, what is the area of the triangle formed by the line 3  [#permalink]

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14 Jul 2017, 09:11
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On solving 3y-4x =24 at y=0 and x=0 u get 8 and -6 . Area will be 1/2 of 48
24
C

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Re: In the XY-plane, what is the area of the triangle formed by the line 3  [#permalink]

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14 Jul 2017, 11:41
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3y -4x =24 implies the line passes through (6,0) and (0,8)
hence area of triangle formed by this line and the two axes is area of a triangle with 6 as base and 8 as height

or 1/2*8*6 = 24
Option C

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Re: In the XY-plane, what is the area of the triangle formed by the line 3  [#permalink]

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14 Jul 2017, 14:34
mynamegoeson wrote:
On solving 3y-4x =24 at y=0 and x=0 u get 8 and -6 . Area will be 1/2 of 48
24
C

Sent from my iPhone using GMAT Club Forum

Hey buddy can you please explain why you used y=0 and x=0? I mean the calculations are clear, but not the logic that's standing behind
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Re: In the XY-plane, what is the area of the triangle formed by the line 3  [#permalink]

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14 Jul 2017, 19:16
1
You use the x-intercept and y intercept as reference points. In simpler questions like this it's all you need to see what the triangle looks like, but in other questions you may have to use both the intercept and actually draw the line to another point.
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Re: In the XY-plane, what is the area of the triangle formed by the line 3  [#permalink]

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14 Jul 2017, 20:10
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cbh wrote:
mynamegoeson wrote:
On solving 3y-4x =24 at y=0 and x=0 u get 8 and -6 . Area will be 1/2 of 48
24
C

Sent from my iPhone using GMAT Club Forum

Hey buddy can you please explain why you used y=0 and x=0? I mean the calculations are clear, but not the logic that's standing behind

Y intercept means the line cuts y axis where x=0

X intercept means the line cuts x axis where y=0

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Re: In the XY-plane, what is the area of the triangle formed by the line 3  [#permalink]

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22 Jul 2018, 02:47
3y -4x =24 implies the line passes through (6,0) and (0,8)
hence area of triangle formed by this line and the two axes is area of a triangle with 6 as base and 8 as height

or 1/2*8*6 = 24
Option C

+1 kudos if you like the post.

niks18 pushpitkc hi there below is my solution but i dont get why i am getting negative value

set x = 0
3y =24
y = 8

set y = 0
-4x=24
x = -$$\frac{24}{4}$$ = $$-6$$

Why everyone is getting positive 6 and i am getting negative -6 ?

Area -6*8 *0.5 = -24

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Re: In the XY-plane, what is the area of the triangle formed by the line 3  [#permalink]

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22 Jul 2018, 02:56
dave13 wrote:
3y -4x =24 implies the line passes through (6,0) and (0,8)
hence area of triangle formed by this line and the two axes is area of a triangle with 6 as base and 8 as height

or 1/2*8*6 = 24
Option C

+1 kudos if you like the post.

niks18 pushpitkc hi there below is my solution but i dont get why i am getting negative value

set x = 0
3y =24
y = 8

set y = 0
-4x=24
x = -$$\frac{24}{4}$$ = $$-6$$

Why everyone is getting positive 6 and i am getting negative -6 ?

Area -6*8 *0.5 = -24

have a great weekend

Hi dave13

When you plot the following points, you will find out that the sides of the
triangle are 8 and 6 respectively. Another thing to add is that the side or
the area can never be a negative number.

So, the area of this triangle is $$\frac{1}{2}*8*6 = 24$$

Hope this helps you!
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Re: In the XY-plane, what is the area of the triangle formed by the line 3   [#permalink] 22 Jul 2018, 02:56
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