Bijesh wrote:
In the rectangular coordinate system, area of the region bounded by three lines x+y=5, x-y=7 , y+13x+7=0 is
Here,
Let's take the equation :
y = -13x -7 as Line 1
y= -x + 5 as Line 2
y = x - 7 as Line 3
We need to find out the point of intersection of these 3 lines
Line 1 and Line 2 meets when x = -1 and y = 6
Line 2 and Line 3 meets when x = 6 and y = -1
Line 1 and Line 3 meets when x = 0 and y =-7
(I have not shown the calculation)
The fig shown below.
Now to find out the area from the 3 lines combined, lets make it a rectangle with co-ordinates (-1,6), (-1,-7) , (6, -7) and (6,6)
Now we need to find out the area of the three right angled triangles formed , they are
yellow \(\triangle\) ,
green \(\triangle\) and
purple \(\triangle\)
For
green \(\triangle\),
Base = 1 , height = 13
Area = \(\frac{1}{2} *1 * 13 = \frac{13}{2}\)
For
purple \(\triangle\)
Area = \(\frac{1}{2} *6 * 6 = 18\)
For
Yellow \(\triangle\)
Area = \(\frac{1}{2}*7 * 7 = \frac{49}{2}\)
Now the area of the rectangle = \(13 * 7 = 91\)
Hence the Area formed by 3 lines =\(91 - (\frac{13}{2} + 18 + \frac{49}{2}) = 42\)
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