Question

find the points of trisection of the line segment (-1,2)and(10,-2)?​

Answer 1

Step-by-step explanation:

Given :-

The points (-1,2) and (10,-2)

To find :-

Find the points of trisection of the linesegment joining the given points ?

Solution :-

Given points are (-1,2) and (10,-2)

Let A = (-1,2)

Let B = (10,-2)

Let the points of Trisection are P and Q

A________P_________Q_________B

We know that

The points which divides the linesegment in the ratio 1:2 or 2:1 are called Trisectional points.

1) Ratio 1:2 :-

Let the point P divides AB linesegment in the ratio 1:2

Let (x1, y1) = (-1,2) => x1 = -1 and y1 = 2

Let (x2, y2) = (10,-2) => x2 = 10 and y2 = -2

Let m1:m2 = 1:2 => m1 = 1 and m2 = 2

We know that

Section formula :-

({m1x2+m2x1}/{m1+m2},{m1y2+m2y1}/{m1+m2})

On Substituting these values in the above formula then

=>P=({(1)(10)+(2)(-1)}/(1+2),{(1)(-2)+(2)(2)}/(1+2))

=> P = ( (10-2)/3} , (-2+4)/3 )

=> P = (8/3 , 2/3)

2)Ratio 2:1:-

Let the point Q divides AB linesegment in the ratio 2:1

Let (x1, y1) = (-1,2) => x1 = -1 and y1 = 2

Let (x2, y2) = (10,-2) => x2 = 10 and y2 = -2

Let m1:m2 = 2:1 => m1 = 2 and m2 = 1

We know that

Section formula

= (({m1x2+m2x1}/{m1+m2},{m1y2+m2y1}/{m1+m2})

On Substituting these values in the above formula then

=>Q=({(2)(10)+(1)(-1)}/(2+1),{(2)(-2)+(1)(2)}/(2+1))

=> Q = ( (20-1)/3} , (-4+2)/3 )

=> Q = (19/3 , -2/3)

Therefore, P (8/3,2/3) and Q(19/3,-2/3)

Answer :-

The Trisectional points of the given linsegment are P (8/3,2/3) and Q(19/3,-2/3)

Used formulae:-

Trisectional points :-

The points which divides the linesegment in the ratio 1:2 or 2:1 are called Trisectional points.

Section formula :-

The coordinates of the point which divides the linesegment joining the points (x1,y1) and (x2, y2) in the ratio m1:m2 is

( {m1x2+m2x1}/{m1+m2} , {m1y2+m2y1}/{m1+ m2} )

Answer 2

Answer:

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