Question

Calculate the ratio in which the line joining A(-4.2) and B(3,6) is divided by point P(x, 3).​

Answer 1

Step-by-step explanation:

Let P(x,3) divide the line segment joining the points A(−4,2) and B(3,6) in the ratio k:1

∴ Coordinates of P is (

m

1

+m

2

m

1

x

2

+m

2

x

1

,

m

1

+m

2

m

1

y

2

+m

2

y

1

)=(

k+1

3k−4

,

k+1

6k+2

)

But coordinate of P is (x,3)

⇒

k+1

6k+2

=3

6k+2=3k+3

3k=1⇒k=

3

1

∴ The required ratio is

3

1

:1 i.e., 1:3 (internally)

∴ Coordinate of P is (

4

−9

,3)

Length of AP=

(x

2

−x

1

)

2

+(y

2

−y

1

)

2

=

(−

4

9

+4)

2

+(3−2)

2

=

(

4

−9+16

)

2

+(1)

2

=

16

49

+1

=

16

49+16

=

16

65

=

4

65

Answer 2

Step-by-step explanation:

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