Oblicz pole trójkata o wierzchołkach
a) A=(-2,4) B=(6,-1) C=(2,-1)
b) K=(-2,3) L= (-2,1) M=(0,0)
POLE TRÓJKĄTA ABC O WIERZCHOŁKACH A= (Xa, Ya), B = (Xb, Yb), C= (Xc, Yc)
PΔ = 1/2 *|(Xb - Xa)(Yc - Ya) - (Yb - Ya)(Xc - Xa)|
PΔ = 1/2 *|(6 - (-2))(-1 - 4) - (-1 - 4)(2 - (-2))|
PΔ = 1/2 *|(6 +2) * (-5) - (-5) * (2 + 2)|
PΔ = 1/2 *|8 * (-5) - (-5) * 4|
PΔ = 1/2 *| -40 - (-20) |
PΔ = 1/2 * | -40 + 20 |
PΔ = 1/2 * (-20)
PΔ = (-10)
PΔ = 1/2 *|(-2 - (-2))(0 - 3) - (1- 3)(0 - (-2)|
PΔ = 1/2 *|(-2 + 2) * (- 3) - (-2)* 2|
PΔ = 1/2 *|0 * (- 3) - (-4)|
PΔ = 1/2 *| - (-4)|
PΔ = 1/2 *4
PΔ = 2
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POLE TRÓJKĄTA ABC O WIERZCHOŁKACH A= (Xa, Ya), B = (Xb, Yb), C= (Xc, Yc)
PΔ = 1/2 *|(Xb - Xa)(Yc - Ya) - (Yb - Ya)(Xc - Xa)|
a) A=(-2,4) B=(6,-1) C=(2,-1)
PΔ = 1/2 *|(6 - (-2))(-1 - 4) - (-1 - 4)(2 - (-2))|
PΔ = 1/2 *|(6 +2) * (-5) - (-5) * (2 + 2)|
PΔ = 1/2 *|8 * (-5) - (-5) * 4|
PΔ = 1/2 *| -40 - (-20) |
PΔ = 1/2 * | -40 + 20 |
PΔ = 1/2 * (-20)
PΔ = (-10)
b) K=(-2,3) L= (-2,1) M=(0,0)
PΔ = 1/2 *|(-2 - (-2))(0 - 3) - (1- 3)(0 - (-2)|
PΔ = 1/2 *|(-2 + 2) * (- 3) - (-2)* 2|
PΔ = 1/2 *|0 * (- 3) - (-4)|
PΔ = 1/2 *| - (-4)|
PΔ = 1/2 *4
PΔ = 2