Question

31) Find the coordinate of the point which divides the line segment joining the

points A(4, -3) and B(9, 7) in the ratio 3:2​

Answer 1

SOLUTION:-

$\sf \red{The \: end \: points \: of \: AB \: are \: A(4,3) \: and \: B(9,7)}$

$\sf \: Fig:- \\ \sf \color{aqua}A•━━━━━━━|━━•B \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: P(x,y)$

$\sf \therefore (x_1=4,y_1=-3) \: and \: (x_2=9,y_2=7)$

$\sf \: Also,m=3 \: and \: n=2$

$\sf \green{ •Let \: the \: required \: point \: be \: P(x,y).}$

$\sf \orange{ •By \: section \: formula \: we \: have \: }$

$\sf \: \: \: x= \frac{(mx_2+nx_1)}{(m+n)} ,y= \frac{(my_2+ny_1)}{(m+n)}$

$\sf ::\implies x= \frac{(3 \times 9 + 2 \times 4)}{(3+2)} ,y= \frac{ \{3×7+2(-3) \}}{(3+2)}$

$\sf:: \implies x=7,y=3$

$\sf \blue{Hence,the \: required \: point \: is \: P(7,3)}$