Question

In what ratio -6,a divides the join of a(-3,-1) and b(-8,9)also find the value of a

Answer 1

Answer:

Step-by-step explanation:

Let the ration be (m/n)=k

So A(-3,-1) and B(-8,9)

(-6,a) = k(-8)+(-3)/k+1 , k(9)+(-1)/k+1

(-6,a) = -8k-3/k+1 , 9k-1/k+1

For getting the ration=

-6=-8k-3/k+1

-6k-6= -8k-3

-6k-6+8k+3=0

2k-3=0

k=3/2 which is the required ratio 3:2

For finding 'a'

a= 9(3/2)-1/(3/2)+1

a= 27/2 -1/5/2

a=25/2*2/5

a= 5

Hope it helps. . . .

Answer 2

$\huge{ANSWER}$

Let's consider the coordinates of a be (x1 ,y1)

and the coordinates of b be (x2,y2).

Let's consider the point dividing these lines be P and the ratio in which they are divided be m1 and m2.

a(-3,-1)___m1__P(-6,a)__m2__b(-8,9)

So, by section Formula we know,

$x = \frac{m1 \times x2 \times + m2 \times x1}{m1 + 2}$

$- 6 = \frac{(m1 \times - 8 )+ (3 \times - 3)}{m1 + m2}$

$- 6m1 + ( - 6m2) = - 8m1 - 3m2$

$- 6m1 - 6m2 = - 8m1 - 3m2$

$- 6m1 + 8m2 = - 3m2 + 6m2$

$2m1 = 3m2$

$\frac{m1}{m2} = \frac{3}{2}$

Hence the ratio in which they are divided is 3 : 2.

So, to find the a,

we know

$x = \frac{m1 \times y2 \times + m2 \times y1}{m1 + 2}$

$a= \frac{3 \times 9 + 2\times - 1}{3 + 2}$

$a = \frac{27 - 2}{5}$

$a = \frac{25}{5}$

$a = 5$

So, the coordinates of P is (-6,5).