Question

a line passes through the points A (2,3) and B(6,7) if the point of AB is p then find the coordinates of p​

Answer 1

Step-by-step explanation:

(i) Since the line joining A(2,3) and B(6,-5) meets the x-axis at P, then the y-coordinate of P is zero(0).

(ii) Let the coordinate of point P is (x,0), also the point P lies between A and B.

Let the ratio of AP:PB be k:1

By section formula,

x=

m

1

+m

2

m

1

x

2

+m

2

x

1

⇒x=

k+1

1.6+k.2

=

k+1

6+2k

and,y=

m

1

+m

2

m

1

y

2

+m

2

y

1

⇒0=

k+1

k.(−5)+1.3

⇒k=

5

3

therefore ratio of AP:PB=3:5

(iii) since P(2,3) is the midpoint of A(x',0) and B(0,y') (from the figure)

∴x=

2

x

1

+x

2

⇒x

′

=4

and,y=

2

y

1

+y

2

⇒y

′

=6

therefore coordinate of A and B is (4,0) and (0,6) respectively.