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Question

Draw the graphs of $$x-y+1=0$$ and $$3x+2y-12=0$$. Determine the coordinates of the vertices of the triangle formed by these lines and $$x$$-axis and shade the triangular area. 


Solution

Given,

$$x-y+1=0$$....(1)

$$3x+2y-12=0$$....(2)

put $$x=0$$ in (1)

$$0-y+1=0\Rightarrow y=1$$

$$(0,1)$$.....(a)

put $$y=0$$ in (2)

$$3x+2(0)-12=0\rightarrow x=4$$

$$(4,0)$$.....(b)

put $$x=0$$ in (2)

$$3(0)+2y-12=0\rightarrow y=6$$

$$(0,6)$$......(c)

put $$y=0$$ in (1)

$$x-0+1=0\Rightarrow x=-1$$

$$(-1,0)$$...(d)

From figure, the vertices of triangle are $$(-1,0),(2,3),(4,0)$$

1433866_966004_ans_4260223fca9d4f269f7e3551126f342d.png

Mathematics

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