Question

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

Answer 1

Answer:

The ratio is $5:3$

Step-by-step explanation:

Let point $(6,-6)$ divides $A(1,4)$ and $B(9,-14)$ in the ratio $m:n$

From the internal division formula

$x=\frac{mx_2+nx_1}{m+n}$

$6=\frac{m\times 9+n\times 1}{m+n}$

$\implies 6(m+n)=9m+n$

$\implies 6m+6n=9m+n$

$\implies 3m=5n$

$\implies \frac{m}{n}=\frac{5}{3}$

$\implies m:n=5:3$

Therefore, the division ratio is $5:3$

Hope the answer is helpful.

Answer 2

Point P divides the line AB in 5:3.

Step-by-step explanation:

Let point P(6, -6) divides the line segment join of A(1, 4) and B(9,-12)​ in k:1.

Section formula:

If a point divides a line segment in m:n, then

$(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n})$

Using section formula the coordinates of point P are

$P=(\dfrac{k(9)+1(1)}{k+1},\dfrac{k(-12)+1(4)}{k+1})$

$P=(9k+1}{k+1},\dfrac{-12k+4}{k+1})$

Coordinates of point P are (6,-6).

$(6,-6)=(9k+1}{k+1},\dfrac{-12k+4}{k+1})$

On comparing both sides we get

$6=\dfrac{9k+1}{k+1}$

$6k+6=9k+1$

$6-1=9k-6k$

$5=3k$

$\dfrac{5}{3}=k$

$k:1=\frac{5}{3}:1=5:3$

Therefore, Point P divides the line AB in 5:3.

#Learn more

Find the coordinates of the point P which divides the join of A(-2,5) and B(3,-5) in the ratio 2:3

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