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 △ ,
green △ and
purple △For
green △,
Base = 1 , height = 13
Area =
12∗1∗13=132For
purple △Area =
12∗6∗6=18For
Yellow △Area =
12∗7∗7=492Now the area of the rectangle =
13∗7=91Hence the Area formed by 3 lines =
91−(132+18+492)=42
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