Question

If A(3,5), B(7,9) and point Q divides seg AB in the ratio 2:3 then find co ordinates of point Q.

Answer 1

Answer:

Note: Section formula:-

If we consider two points, say A(x1,y1) and B(x2,y2) & let a point Q(x,y) which internally divides the segment AB in ratio m:n , then the coordinates of point O is given by:

x = (mx2 + nx1)/(m + n)

y = (my2 + ny1)/(m + n)

Here,

It is given that;

The coordinates of point A is (3,5)

The coordinates of point B is (7,9)

Clearly,

x1 = 3 , y1 = 5

x2 = 7 , y2 = 9

Also,

m:n = 2:3

Let the coordinates of point Q be (x,y)

Then,

As per section formula we have;

=> x = (mx2 + nx1)/(m + n)

=> x = (2•7 + 3•3)/(2 + 3)

=> x = (14 + 9)/5

=> x = 23/5

Similarly,

=> y = (my2 + ny1)/(m + n)

=> y = (2•9 + 3•5)/(2 + 3)

=> y = (18 + 15)/5

=> y = 33/5

Hence, the required coordinates of point Q is (23/5 , 33/5).

Answer 2

Answer:

let A(3,5 )=(x1, y1 )

B(7,9 )=( x2,y2)

m:n=2:3. then, m=2,n=3

by section formula =

x=mx2+nx1/m+n

y=ny2+ny1/m+n

by substituting the values

x=2x7+3x3/2+3

y=29+3x5/2+3

x=14+9/5

y=18+15/5

x=23/5

y=33/5