Question

Question 1
a) A straight line passes through the point P(-3,4) and intersects the co-ordinate axes
at A and B. The point P divides the line AB in the ratio 2:3. Find the coordinates of A
and B
B
[3]
P.
o
X
can​

Answer 1

Answer:

A(- 5, 0) ; B(0, 10)

Step-by-step explanation:

P( $\frac{mx_{2} +nx_{1} }{m+n}$ , $\frac{my_{2} +ny_{1} }{m+n}$ ) = P( - 3, 4)

AP : PB = m : n = 2 : 3

$\frac{2x_{2} +3x_{1} }{5}$ = - 3 ⇒ 2$x_{2}$ + 3$x_{1}$ = - 15 .... (1)

$\frac{2y_{2} +3y_{1} }{5}$ = 4 ⇒ 2$y_{2}$ + 3$y_{1}$ = 20 .... (2)

Because coordinates of P are whole numbers

(1) ⇒ $x_{2}$ = 0 and $x_{1}$ = - 5

(2) ⇒ $y_{1}$ = 0 and $y_{2}$ = 10

A(- 5, 0) and B(0, 10)