Math, asked by Aquarusherstar, 5 months ago

The line segment joining the points (3,-4)and (1,2)is
trisected at the points P and Q. If the coordinates of P and Q are (p,-2) and (5/3,q) respectively. Fimd the value of P and Q. ​

Answers

Answered by kumard75182
2

Answer:

Suppose Points P and Q trisect the line segment joining the pointsA(3,−4) and B(1,2)

This means, P divides AB in the ratio 1:2 and Q divides it in the ratio 2:1

Using the section formula, if point (x,y) divides the line joining the points (x

1

,y

1

) and (x

2

,y

2

) internally in the ratio m:n, then(x,y)=(

m+n

mx

2

+nx

1

,

m+n

my

2

+ny

1

)

Substituting (x

1

,y

1

)=(3,−4) and (x

2

,y

2

)=(1,2) and m=1,n=2 in the section formula, we get the point P =(

1+2

1(1)+2(3)

,

1+2

1(2)+2(−4)

)=(

3

7

,−2)

Given. P(p,−2)=(

3

7

,−2)

=>p=

3

7

Substituting (x

1

,y

1

)=(3,−4) and (x

2

,y

2

)=(1,2) and m=2,n=1 in the section formula, we get the point Q =(

2+1

2(1)+1(3)

,

2+1

2(2)+1(−4)

)=(

3

5

,0)

Given. Q(

3

5

,0)=(

3

5

,q)

=>q=0

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