Question

FIND THE RATIO IN WHICH THE POINT (2,y) DIVIDES THE LINE SEGMENT JOINING THE POINTS A(-2,2) & B(3,7) . ALSO FIND THE VALUE OF ' y' ?

Answer 1

$ratio = 4 : 1 \\ \\ or \: \dfrac{m}{n} = \dfrac{4}{1} \\ \\ \\ also \\ \\ value \: of \: y \: is \: equal \: to \: 5$

Please refer the above photographs for the used process.

KEY POINTS TO REMEMBER :-

☸️ SECTION FORMULA :-

The coordinates of a point which divides a line A (x1, y1) and B (x2, y2) in ratio equal to m:n is expressed as :-

$x = \dfrac{mx_2 + nx_1}{m + n} \\ \\ y = \dfrac{my_2 + ny_1}{m + n} \\ \\ \\ \\ this \: is \: the \: section \: formula$

☸️ Also, The reverse of this section formula is used to find the ratio in which the line is divided by the given points.

(CONVERSE OF SECTION FORMULA)

THANKS!