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

Question

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

broall · Answer

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 $\frac{6*8}{2}=24$

The answer is C

Mujeeb · Answer

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

Answer is C

Luckisnoexcuse · Answer

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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sonikavadhera · Answer

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.

cbh · Answer

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

grassmonkey · Answer

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.

Luckisnoexcuse · Answer

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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dave13 · Answer

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

pushpitkc · Answer

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!

bumpbot · Answer

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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

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