Question

anyone know this question?

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Answer 1

k : 1

(-5,-4) •-----------•------------------• ( -2,3)

A C(-3, p) B

Let the ratio in which point C divides the line segment AB be k : 1

Now,

( m1x2 + m2x1 ) / (m1 + m2 ) = -3

==> -2k -5 / k + 1 = -3

==> -2k - 5 = -3k - 3

==> k = 5 - 3

==> k = 2

Hence, The Point C divides the line segment AB in the ratio 2 : 1

Now,

==> (m1y2 + m2y1) / (m1 + m2) = p

==> ( 2 * 3 + 1*-4 ) / (2 + 1) = p

==> 6 - 4 / 3 = p

==> p = 2/3

Answer 2

Answer:

Let P(-3,p) divide the line segment joining the points A(-5,-4) and B(-2,3) in the ratio k:1

Using section formula

$P(-3,p) = (\frac{kx_{2}+ x_{1}}{k+1} , \frac{ky_{2}+y_{1}}{k+1})\\ = (\frac{-2k-5}{k+1}, \frac{3k-4}{k+1})$

Comparing the value of x-coordinate

$-3=\frac{-2k-5}{k+1} \\-3(k+1)=-2k-5\\-3k-3=-2k-5\\-3k+2k=-5+3\\-k=-2\\k=2$

Therefore, P(-3,p) divides the line segment in the ratio 2:1

Substituting the value of k in y-coordinate

$p=\frac{3*2-4}{2+1} \\\\p=\frac{6-4}{3} \\p=\frac{2}{3}$

Therefore p=2/3 and the coordinates of P are (-3,2/3)

Here ya go