Question

What are the coordinates of the point 3/4 of the way from A toB?

Answer 1

Answer:

( -3 , 4)

–

4

Step-by-step explanation:

Let P be the point which is three-fourth of the way from A(3,1) to B(−2,5).

∴AP:AB=3:4

AB=AP+PB

∴

AB

AP

=

(AP+PB)

AP

=

4

3

⇒4AP=3AP+3PB

⇒4AP−3AP=3PB

⇒AP=3PB

$$\Rightarrow \dfrac{AP}{AB} = \dfrac{3}{1}$$

∴ The ratio m:n=3:1

x

1

=3,y

1

=1,x

2

=−2,y

2

=5

∴ By Section formula x=

m+n

mx

2

+nx

1

∴x=

3+1

3×−2+1×3

∴x=

4

−6+3

∴x=

4

−3

And

∴ By Section formula y=

m+n

my

2

+ny

1

∴y=

3+1

3×5+1×1

∴y=

4

15+1

∴y=4

Hence the co-ordinates of P are ( -3 , 4)

–

4