Point A lies in a plane, point B is at a distance of 12.5 m from this plane. Find the distance from the plane to the point M dividing the segment AB in the ratio AM: MB = 2: 3.
Triangles ACM and AOB are similar. Since angle A is common, MC is parallel to OB. Let AB = x, then AM = (2/5) x, MB = (3/5) x.
AM: MВ = 2: 3.
From the similarity we get: AB: BO = AM: MC, that is, x / 12.5 = (2/5) x: 5 / (x ^ 2) = (2/5) x * (x ^ 2) / 5. x / 12.5 = 2x ^ 3 / 25. Reduce by x. We get: 1 / 12.5 = 2x ^ 2 / 25. Multiply both sides of the equation by 12.5. We get: 1 = x ^ 2. The equation has 2 roots: 1 and -1.
MC = 5 / (x ^ 2) = 5/1 = 5.
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