Question

FIND THE COORDINATES OF THE POINT WHICH IS THREE-FOURTH OF WAY FROM A(3,1) TO B(-2,5)​

Answer 1

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

∴ABAP=(AP+PB)AP=43

⇒4AP=3AP+3PB

⇒4AP−3AP=3PB

⇒AP=3PB

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

∴ The ratio m:n=3:1

x1=3,y1=1,x2=−2,y2=5

∴ By Section formula x=m+nmx2+nx1

∴x=3+13×−2+1×3

∴x=4−6+3

∴x=4−3

And

∴ By Section formula