Question

Find the ratio in which the point P(-2,-1) divides the segment joining the points (-5,2) and (2,-5)​

Answer 1

Answer:

Let the ratio be k:1.

A=(-5,2), B=(2,-5), P=(-2,-1)

x=(-2), x1=(-5), x2=2,y=(-1), y1=2, y2=(-5), m1=k, m2=1

$x = \frac{m1 x2 + m2x1}{m1 + m2} </p><p>$$( - 2) = \frac{k(2) + 1( - 5)}{k + 1}$

$( - 2)(k + 1) = k(2) + 1( - 5)$

$( - 2k) - 2 = 2k - 5$

$( - 2k) - 2k = ( - 5) + 2$

$( - 4k) = ( - 3)$

$4k = 3$

$\frac{k}{1} = \frac{3}{4}$

k:1=3:4

Therefore, the ratio in which the point P divides the segment AB is 3:4

Answer 2

Let the ratio be k:1.

A=(-5,2), B=(2,-5), P=(-2,-1)

x=(-2), x1=(-5), x2=2,y=(-1), y1=2, y2=(-5), m1=k, m2=1

x = \frac{m1 x2 + m2x1}{m1 + m2} < /p > < p >x=

m1+m2

m1x2+m2x1

</p><p> ( - 2) = \frac{k(2) + 1( - 5)}{k + 1}(−2)=

k+1

k(2)+1(−5)

( - 2)(k + 1) = k(2) + 1( - 5)(−2)(k+1)=k(2)+1(−5)

( - 2k) - 2 = 2k - 5(−2k)−2=2k−5

( - 2k) - 2k = ( - 5) + 2(−2k)−2k=(−5)+2

( - 4k) = ( - 3)(−4k)=(−3)

4k = 34k=3

\frac{k}{1} = \frac{3}{4}

1

k

=

4

3

k:1=3:4

Therefore, the ratio in which the point P divides the segment AB is 3:4