CAS View Supported Geometry Commands
From GeoGebra Manual
CAS View Supported Geometry Commands
From GeoGebra 4.9.170.0 on, the CAS View supports exact versions of the following Geometry Commands.
Exact Calculations
Command | Evaluate | Numeric or Input, Rounding 2 Decimal Places |
---|---|---|
Angle[(1,0),(0,0),(1,2)] | arctan \left( 2 \right) | Numeric : 1.11 Input : 63.43° or 1.11 rad according Angle Unit selected |
AngleBisector[(0,1),(0,0),(1,0)] | y = x | Numeric : y = x Input : - 0.71 x +0.71 y = 0 |
Circumference[x^2+y^2=1/sqrt(π)] | 2 \; \sqrt{\pi \; \sqrt{\pi}} | 4.72 |
Distance[(0,0), x + y = 1] Simplify[Distance[(0,0), x+y=1]] |
\frac{1}{\sqrt{2}} \frac{\sqrt{2}}{2} |
0.71 |
Distance[(0,0),x+2y=4] Simplify[Distance[(0,0),x+2y=4]] |
\frac{4}{\sqrt{5}} 4 \cdot \frac{\sqrt{5}}{5} |
1.79 |
Distance[(0,4),y=x^2] Simplify[Distance[(0,4),y=x^2]] |
\sqrt{ \left( \frac{7}{2} - 4 \right)^{2} + \left( -\frac{1}{2} \; \sqrt{14} \right)^{2}} \frac{\sqrt{15}}{2} |
1.94 |
Distance[(0.5,0.5),x^2+y^2=1] Simplify[ Distance[(0.5,0.5),x^2+y^2=1]] |
\frac{\frac{1}{\sqrt{2}}}{\sqrt{2}} \; \sqrt{ \left( -\sqrt{2} + 1 \right) \; \left( -\sqrt{2} + 1 \right) \; \sqrt{2} \; \sqrt{2}} \frac{-\sqrt{2} + 2}{2} |
0.29 |
Ellipse[(2,1),(5,2),(5,1)] | 28 \; x^{2} - 24 \; x \; y - 160 \; x + 60 \; y^{2} - 96 \; y + 256 = 0 | Numeric : 28 \; x^{2} - 24 \; x \; y - 160 \; x + 60 \; y^{2} - 96 \; y + 256 = 0 Input : 7 \; x^{2} - 6 \; x \; y + 15 \; y^{2} - 40 \; x + - 24 \; y = - 64 |
Ellipse[(2,1),(5,2),(6,1)] | 32 \; x^{2} \; \sqrt{2} + 36 \; x^{2} - 224 \; x \; \sqrt{2} - 24 \; x \; y - 216 \; x \; ... \; ... + 32 \; \sqrt{2} \; y^{2} - 96 \; \sqrt{2} \; y + 256 \; \sqrt{2} + 68 \; y^{2} - 120 \; y + 196 = 0 |
Numeric : 81.25 \; x^{2} - 24 \; x \; y - 532.78 \; x + 113.25 \; y^{2} - 255.76 \; y + 558.04 = 0 Input : 81.25 \; x^{2} - 24 \; x \; y - 532.78 \; x + 113.25 \; y^{2} - 255.76 \; y = - 558.04 |
Radius[x^2+y^2=1/sqrt(π)] | \frac{\sqrt{\pi \; \sqrt{\pi}}}{\pi} | 0.75 |
Symbolic Computations
Command | Evaluate | Numeric |
---|---|---|
Circle[(a,b),r] | (y - b)² + (x - a)² = r² | |
Distance[(a,b),(c,d)] | \sqrt{ \left( b - d \right)^{2} + \left( a - c \right)^{2}} | \sqrt{a^{2} - 2 \; a \; c + b^{2} - 2 \; b \; d + c^{2} + d^{2}} |
Distance[(a,b),p x + q y = r] | ||
Line[(a,b),(c,d)] | y = \frac{x}{a - c} \; \left( b - d \right) + \frac{1}{a - c} \; \left( a \; d - b \; c \right) | y = \frac{a \; d - b \; c + b \; x - d \; x}{a - c} |
Line[(a,b),y=p x+q] | y = p x - a p + b | y = -a p + b + p x |
MidPoint[(a,b),(c,d)] | \left( \frac{a + c}{2}, \frac{b + d}{2} \right) | \left( 0.5 \; a + 0.5 \; c, 0.5 \; b + 0.5 \; d \right) |
PerpendicularBisector[(a,b),(c,d)] | y = \frac{-a + c}{b - d} \; x + \frac{a^{2} + b^{2} - c^{2} - d^{2}}{2 \; b - 2 \; d} | y = \frac{a^{2} - 2 \; a \; x + b^{2} - c^{2} + 2 \; c \; x - d^{2}}{2 \; b - 2 \; d} |