Points M and N lie on opposite sides of the straight line “a” at a distance of 2 cm and 3 cm.

| June 21, 2021 | education

Points M and N lie on opposite sides of the straight line “a” at a distance of 2 cm and 3 cm. Find the distance between the projections of these points on the straight line if MN = 13 cm

Let point O be the point of intersection of lines MH and AB.

Triangles AOM and ВOН are rectangular, in which the angle AOM = ВOН as vertical angles, then the triangles AOM and ВOН are similar in acute angle.

Let the length of the segment OM = X cm, then OH = (13 – X) cm.

From the similarity of triangles AM / OM = ВН / OH.

2 / X = 3 / (13 – X).

3 * X = 26 – 2 * X.

5 * X = 26.

X = OM = 5.2 cm, OH = 13 – 5.2 = 7.8 cm.

In a right-angled triangle AOM, according to the Pythagorean theorem, OA ^ 2 = OM ^ 2 – AM ^ 2 = 27.04 – 4 = 23.04.

OA = 4.8 cm.

Then ОВ = 3 * ОА / 2 = 3 * 4.8 / 2 = 7.2 cm.

AB = OA + OB = 4.8 + 7.2 = 12 cm.

Answer: The distance between the projections of the points is 12 cm.



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