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photoshop1234 [79]
3 years ago
9

What are the points of trisection of the segment with endpoints (0,0) and (27,27) ?

Mathematics
1 answer:
stiks02 [169]3 years ago
6 0

Given:

Endpoints of a segment are (0,0) and (27,27).

To find:

The points of trisection of the segment.

Solution:

Points of trisection means 2 points between the segment which divide the segment in 3 equal parts.

First point divide the segment in 1:2 and second point divide the segment in 2:1.

Section formula: If a point divides a line segment in m:n, then

Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)

Using section formula, the coordinates of first point are

Point\ 1=\left(\dfrac{1(27)+2(0)}{1+2},\dfrac{1(27)+2(0)}{1+2}\right)

Point\ 1=\left(\dfrac{27}{3},\dfrac{27}{3}\right)

Point\ 1=\left(9,9\right)

Using section formula, the coordinates of first point are

Point\ 2=\left(\dfrac{2(27)+1(0)}{2+1},\dfrac{2(27)+1(0)}{2+1}\right)

Point\ 2=\left(\dfrac{54}{3},\dfrac{54}{3}\right)

Point\ 2=\left(18,18\right)

Therefore, the points of trisection of the segment are (9,9) and (18,18).

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