Calculate the area of ​​a figure bounded by lines x-y+3=0 x+y-1=0 y=0

cuuhorre76 2022-09-11 Answered
Calculate the area of ​​a figure bounded by lines
x-y+3=0 x+y-1=0 y=0
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Answers (1)

Clarence Mills
Answered 2022-09-12 Author has 18 answers
Three lines form a triangle.
The line x-y+3=0 passes through the points (-3; 0) and (0; 3)
The line x+y-1=0 passes through the points (0;1) and (1;0)
y=0 - the equation of the x-axis.
Direct
x-y+3=0 and
x+y-1=0
intersect at x=1 y=2
Triangle isosceles
Base from point -3 to point 1
The height passes through the intersection point x=1 y=2 and is equal to the ordinate of this point
S=1/2 4 2=4 sq. units
Second way
S = 3 1 ( x + 3 ) d x + 1 1 ( x + 1 ) d x = ( x 2 2 + 3 x ) 3 1 + ( x 2 2 + x ) 1 1 =
= 1 2 3 ( 9 2 9 ) + ( 1 2 + 1 ) ( 1 2 1 ) = 4

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