Question

Given the points A(-3,-4) and B(2,0), point P(-1,-12/5) partions AB in the ratio

Answer 1

Answer:

2:3

Step-by-step explanation:

Given: Points A(-3,-4) and B(2,0), point P(-1,-12/5)

To find: The ratio in which P divide AB

Solution:

We know that the coordinate of a point $(x,y)$ dividing a line segment joining $(x_{1},y_{1}) \:\text{and} (x_{2},y_{2})$ in the ratio m:n is given by

$x=\frac{mx_{2}+nx_{1}}{m+n}$, $y=\frac{my_{2}+ny_{1}}{m+n}$

Now, let the ratio be k:1

Here, coordinate of P is $(-1,\frac{-12}{5} )$

So, $-1=\frac{ k(2)+1(-3)}{k+1}$

$-k-1=2k-3$

$2k+k=3-1$

$3k=2$

$k=\frac{2}{3}$

Hence, the ratio is 2:3.

Answer 2

The x-coordinate of P (-1) is 2 units from that of A and 3 units from that of B.

P partitions AB in the ratio 2:3.