Question

1 Find the pont of trisection of the line
segment joining the points (3-2 ) and (3-2)​

Answer 1

Answer:

Let P and Q be the point of trisection of AB such that AP = PQ = QB So, P divides AB internally in the ratio of 1: 2, thereby applying section formula, the coordinates of P will be Now, Q also divides AB internally in the ratio of 2:1 so their coordinates will be (ii) Let P and Q be the points of trisection of AB such that AP = PQ = QB As, P divides AB internally in the ratio of 1: 2. Hence by applying section formula, the coordinates of P are Now, Q also divides as internally in the ratio of 2: 1 So, the coordinates of Q are given by (iii) Let P and Q be the points of trisection of AB such that AP = PQ = OQ As, P divides AB internally in the ratio 1:2. So, the coordinates of P, by applying the section formula, are given by Now. Q also divides AB internally in the ration 2: 1.

Answer 2

Step-by-step explanation:

Given:-

Points are (3,-2 ) and (3,-2)

To find:-

Find the pont of trisection of the line

segment joining the points (3,-2 ) and (3,-2) ?

Solution:-

Given points are (3,-2 ) and (3,-2)

Let A=(3,-2 ) and B = (3,-2 )

Let (x1, y1)=(3,-2)=> x1=3 and y1 = -2

Let (x2, y2)=(3,-2)=>x2=3 and y2=-2

Trisectional points:-

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

Now

Let the Trisectional points be P and Q

A________P________Q________B

AP : PB = 1:2

BQ : QA = 2:1

I) Coordinates of P:-

On taking ratio 1:2

Let (x1, y1)=(3,-2)=> x1=3 and y1 = -2

Let (x2, y2)=(3,-2)=>x2=3 and y2=-2

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

We know that

Section formula

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

=> ( {(1×3)+(2×3)}/{1+2}, {(1×-2)+(2×-2)}/{1+2} )

=> ( {3+6}/3 , {-2-4}/3 )

=> ( 9/3 , -6/3 )

=> (3 , -2 )

The coordinates of P = (3,-2)

Coordinates of Q:-

On taking ratio 2:1

Let (x1, y1)=(3,-2)=> x1=3 and y1 = -2

Let (x2, y2)=(3,-2)=>x2=3 and y2=-2

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

We know that

Section formula

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

=> ( {(2×3)+(1×3)}/{2+1}, {(2×-2)+(1×-2)}/{2+1} )

=> ( {6+3}/3 , {-4-2}/3 )

=> ( 9/3 , -6/3 )

=> (3 , -2 )

The coordinates of Q = (3,-2)

Answer:-

The Trisectional points of the given linesegment are (3,-2) and (3,-2)

Used formula:-

Section formula:-

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

• The points which divides the given linesegment into three equal parts (or) The points which divides the given linesegment in the ratio 1:2 or 2:1 are called Trisectional points or the Points of Trisectional.