Question

The ratio in which the point P(6, -6) divides
in which the point P16, -6) divides the join of A(1, 4) and B(9,-12)​

Answer 1

Answer:

ratio is 5:3

Step-by-step explanation:

let the ratio be k:1

then,

9k+1/(k+1)=6

9k+1=6(k+1)

9k+1=6k+6

3k=5

k=5/3

Answer 2

Answer:

5:3

Step-by-step explanation:

Let us assume that, the point P(6,-6) divides the line joining the points A(1,4) and B(9,-12) internally.

So, the length of AP will be given by $\sqrt{(6-1)^{2}+(-6-4)^{2}  } =\sqrt{25+100}=\sqrt{125}  =5\sqrt{5}$

Similarly again the length of BP will be given by  $\sqrt{(6-9)^{2}+(-6+12)^{2}  } =\sqrt{9+36}=\sqrt{45}  =3\sqrt{5}$.

Hence, AP:BP =5√5 : 3√5 =5:3.

Therefore, the point P divides AB in the ratio 5:3 internally.

(Answer)