Coordinate axes

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

Result

S =  40.5

Solution:

−7x+7y+63=0  x=0: −7⋅ 0+7y+63=0 7y=−63 y=−63/7=−9   y=0: −7x+7⋅ 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⋅ b/2=9⋅ 9/2=812=40.5-7x + 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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Tips to related online calculators
For Basic calculations in analytic geometry is helpful line slope calculator. From coordinates of two points in the plane it calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of segment, intersections the coordinate axes etc.
See also our right triangle calculator.
Do you want to convert length units?
See also our trigonometric triangle calculator.

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