已知三角形的三个顶点A(2,-1,4)、B(3,2,-6)、C(-5,0,2),求过点

已知三角形的三个顶点A(2,-1,4)、B(3,2,-6)、C(-5,0,2),求过点A的中线长.

答案

解析:

中线长是一个顶点与其对边中点连线段的长,所以可由中点坐标公式求出对边中点,再代入两点间距离公式计算.

答案:

先求边BC的中点M,再利用两点间的距离公式求A、M间的距离.

M(),化简得M(-1,1,-2).

中线,所以过点A的中线长为7.

注意:空间中两点A(x1,y1,z1)、B(x2,y2,z2)的中点坐标和平面上两点的中点坐标公式类似,应为M().

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