Question

The point R divides the line-segment AB, where A(– 4, 0) and B(0, 6) are such that AR = 3 4 AB. Find the coordinates of R.

Answer 1

your question is wrong it is 3AR=4AB
can this is correct answer

Answer 2

Answer:   $(-1, 4.5)$

Step-by-step explanation:

Since, AR = 3/4 AB

AR = 3/4 ( AR + BR )

4 AR = 3 AR + 3 BR

AR = 3 BR

AR : BR = 3 : 1

Hence, the point R divides the line segment AB in the ration of 3:1

Where, the co-ordinates of A is (-4,0) and  the co-ordinates of B is (0,6) ,

Thus, by the section formula,

The coordinates of R are,

$(\frac{3\times 0 + 1\times -4}{3+1}, \frac{3\times 6+1\times 0}{3+1})$

$(\frac{-4}{4},\frac{18}{4})$

$(-1, 4.5)$