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求点到平面的距离是高考热点问题,直线与平面间的距离,两平行平面间的距离,都可以转化为点到平面的距离来解决.下面介绍几种点到平面的距离的求法.一、直接法1.利用空间图形的性质寻求垂足的位置,直接向平面引垂线,构造三角形求解.例1已知ΔABC,AB=9,AC=15,∠BAC=120°,ΔABC所在平面α外一点P到此三角形三个顶点的距离都是14,求点P到α的距离.
Finding the distance from the point to the plane is a hot issue in the college entrance examination. The distance between the straight line and the plane, and the distance between the two parallel planes, can all be converted into point-to-plane distances. The following describes how to determine the distance from point to plane. Direct method 1. Use the nature of the space graph to seek the position of the foot, direct the perpendicular to the plane, construct a triangle solution. Example 1 Known ΔABC, AB=9, AC=15, ∠BAC=120°, ΔABC where the plane The distance from α to P to the three vertices of this triangle is 14 and the distance from P to α is calculated.