Question

EXERCI
13+ 12 2
1. Calculate the co-ordinates of P which divides
the join of:
(i) A(6, 8) and B(1, -2) in the ratio 3:2.
(ii) A(5, -1) and B(-2, -15) in the ratio 2:5.
(iii) A(0,5) and B(5, 20) in the ratio 3 : 2.
1 D/​

Answer 1

$\sf\huge\underline{Answer:}$

Let coordinates of P be x and y = P(x, y)

(i) A(6, 8) and B(1, -2) ; ratio = 3:2

We have to use the section formula,

$P(x, y) = (\frac{m x_{2} + nx_{1}}{m + n} , \frac{m y_{2} + ny_{1}}{m + n} )$

$= (\frac{3(1) + 2(6)}{3 + 2}, \frac{3( - 2) + 2(8)}{3 + 2} )$

$= (3,2)$

(ii) A(5, -1) and B(-2, -15) ; ratio = 2:5

$P(x, y) = (\frac{m x_{2} + nx_{1}}{m + n} , \frac{m y_{2} + ny_{1}}{m + n} )$

$= (\frac{2( - 2) + 5(5)}{2 + 5} , \frac{2( - 15) + 5( - 1)}{2 + 5} )$

$= (3, - 5)$

(iii) A(0, 5) and B(5, 20) ; ratio = 3:2

$P(x, y) = (\frac{m x_{2} + nx_{1}}{m + n} , \frac{m y_{2} + ny_{1}}{m + n} )$

$=( \frac{3(5) + 2(0)}{3 + 2} ,\frac{3(20) + 2(5)}{3 + 2} )$

$= (3,14)$

$\sf{Have~a~good~evening~!}$