Question

Q45. If the point B(- 2, 4) divides internally the line segment joining the points A
(2,5) and C(x, y) in the ratio of 3:4, find the value of x2 + y2.​

Answer 1

Answer:

We know that by section formula, the co-ordinates of the points which divide internally the line segment joining the points (x

1

,y

1

) and (x

2

,y

2

) in the ratio m:n is

(x,y)=(

m+n

mx

2

+nx

1

,

m+n

my

2

+ny

1

)

Since, C divides A & B in the ratio 3:4 internally

By section formula

3+4

3x+4(2)

=−1,

3+4

3y+4(5)

=2

⇒3x+8=−7, 3y+20=14

x=

3

−15

, 3y=−6

⇒x=−5, y=−2

x

2

+y

2

=(−5)

2

+(−2)

2

=25+4

∴x

2

+y

2

=29.