Question

If C is a point lying on the line segment AB joining A(1, 1) and B(2, – 3) such that 3AC =
CB, then find the coordinates of C.

Answer 1

$\huge\pink{\boxed{\blue{\boxed{ \purple{ \boxed{{\pink{Answer}}}}}}}} \\ \large\pink{\boxed{\blue{\boxed{ \purple{ \boxed{{\pink{Your~answer↓}}}}}}}}$

Given :-

A line segment AB such that coordinates of A and B are (1, 1) and (2, -3). C is any point on AB such that 3AC = BC.

To find :-

Coordinates of C.

Formula used :- Section Formula

Solution :-

Since C is point on AB such that 3AC = BC

=> AC : BC = 1 : 3

=> C divides AB jn the ratio 1:3.

$\ \fcolorbox{black}{c}{♛So, using section formula♛}$

Coordinates of C are

$\small\bold\red{( \frac{1 \times 2 + 3 \times 1}{1 + 3} , \frac{1 \times ( - 3) + 3 \times 1}{1 + 3} )} \\ \small\bold\red{ = ( \frac{2 + 3}{4} , \frac{ - 3 + 3}{4} )} \\ \small\bold\red{ = ( \frac{5}{4}, 0 )}$

$\ \fcolorbox{black}{yellow}{♛hope \: it \: helps \: you♛}$