Question

find the coordinates of the points of trisection of line joining the points (6,-2) and (10,8)​

Answer 1

Answer:

s

m

=

2

1

Thus P divides AB in the ratio 1:2

Now, we have to find P

Let P be (x,y)

Hence,

m

1

=1, m

2

=2

And for AB

x

1

=2, x

2

=−2

y

1

=−7, y

2

=4

x=

m

1

+m

2

m

1

x

2

+m

2

x

1

=

1+2

1×(−7)+2×2

=

3

−7+4

=−1

y=

m

1

+m

2

m

1

x

2

+m

2

x

1

=

1+2

1×4+2×(−2)

=

3

4−4

=0

Hence, point P is P(−1,0)

Similarly, Point A divides AB in the ratio AQ & QB

=

QB

AQ

=

QB

AP+PQ

=

k

k+k

=

1

2

=2:1

Now, we have to find Q

Let Q be (x,y)

Hence,

m

1

=2, m

2

=1

x

1

=2, x

2

=−2

y

1

=−7, y

2

=4

x=

m

1

+m

2

m

1

x

2

+m

2

x

1

=

1+2

2×(−7)+1×2

=

3

−14+2

=−4

y=

m

1

+m

2

m

1

x

2

+m

2

x

1

=

1+2

2×4+1×(−2)

=

3

8−2

=2

Answer 2

Answer:

p(22/3, 2) and q(26/3, 14/3)