Question

Find the distance pq. Find the coordinates of the point which divides the line segment joining the points p and q internally in the ratio 2:3

Answer 1

Answer:

(i) Internally: h=

m+n

mx

2

+nx

1

, k=

m+n

my

2

+ny

1

, l=

m+n

mx

2

+nx

1

h=

2+3

2(3)+3(1)

,k=

2+3

2(4)+3(−2)

,l=

2+3

2(−5)+3(3)

h=

5

9

,k=

5

2

,l=

5

−1

c(

5

9

,

5

2

,

5

−1

).

(ii) Externally:

h=

m−n

mx

2

−nx

1

,k=

m−n

my

2

−ny

1

,l=

m−n

mx

2

−nx

1

h=

2−3

2(3)−3(1)

,k=

2−3

2(4)−3(−2)

,l=

2−3

2(−5)−3(3)

h=

−1

3

,k=

−1

14

,l=

−1

−19

c(−3,−14,19).

solution