Coordinate axes

Determine the area of the triangle given by line -7x+7y+63=0 and coordinate axes x and y.

Correct result:

S =  40.5

Solution:

$-7x + 7y + 63=0 \ \\ \ \\ x=0: \ \\ -7 \cdot \ 0+7y + 63=0 \ \\ 7y=-63 \ \\ y=-63 / 7=-9 \ \\ \ \\ \ \\ y=0: \ \\ -7x+7 \cdot \ 0 + 63=0 \ \\ 7x=63 \ \\ x=63 / 7=9 \ \\ \ \\ \ \\ a=|x|=|9|=9 \ \\ b=|y|=|(-9)|=9 \ \\ \ \\ ABC: (0,0), (0,-9), (9,0) \ \\ \ \\ S=a \cdot \ b / 2=9 \cdot \ 9 / 2=\dfrac{ 81 }{ 2 }=40.5$

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