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三角形面積

y. B ( x 2 , y 2 ). P. R. A ( x 1 , y 1 ). x. S. C ( x 3 , y 3 ). 三角形面積. 長方形 PRSC 面積 = ( x 1 - x 3 ) ( y 2 - y 3 ). ( x 3 , y 2 ). ( x 1 , y 2 ). D BRA 面積 = 1/2( x 1 - x 2 ) ( y 2 - y 1 ). D ASC 面積 = 1/2( x 1 - x 3 ) ( y 1 - y 3 ).

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三角形面積

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  1. y B(x2 , y2) P R A(x1 , y1) x S C(x3 , y3) 三角形面積 長方形PRSC面積 = (x1 - x3 ) (y2 - y3 ) (x3 , y2) (x1 , y2) DBRA面積= 1/2(x1 - x2 ) (y2 - y1 ) DASC面積= 1/2(x1 - x3 ) (y1 - y3 ) DPBC面積= 1/2(x2 - x3 ) (y2 - y3 ) DABC面積= 1/2(x1 y2 +x2y3 +x3y1 - x2 y1 - x3y2 -x1y3 ) (x1 , y3)

  2. y 逆時針方向 B(x2 , y2) - x1 y3 - x3 y2 - x2 y1 + x1 y2 + x2 y3 + x3 y1 A(x1 , y1) x C(x3 , y3) x1 y1 x2 y2 DABC面積= 1/2 x3 y3 x1 y1 DABC面積= 1/2(x1 y2 +x2y3 +x3y1 - x2 y1 - x3y2 -x1y3 ) =1/2[(x1 y2 - x2 y1)+(x2y3 - x3y2)+ (x3 y1 -x1y3 )] x1 y1 x2 y2 x3 y3 x1 y1

  3. y A(-1, 5) B(-4, 1) x C(2, -1) 例子 找出由頂點 A(-1, 5), B(-4, 1) and C(2, -1).所組成雞三角形面積 DABC面積= = 15平方單位 DABC面積= = -15平方單位

  4. Example 2 己知三點為A(0, -8), B(1, -2) and C(3, k) ，三點均在同一直線上。試找k的值。 幾何意義

  5. 例子3 已知A(0, 4) , B(2, 6)和C(-2, k). 若ABC的面積為4平方單位，試求k的值。 幾何意義

  6. Example 4 已知ABC的頂點為A(3, 2), B(-1, 1)和 C(5, -4). 試找出由A到BC的垂直距離。

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