Question

Find the ratio in which the point X (-6, h) divides the join of P (-4, 4) and Q (6, -1) and here hence find the value of h.
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Answer 1

Answer:

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Answer 2

Answer:

The ratio in which the point divides PQ = 1:6

The value of h = 5

Step-by-step explanation:

To find,

The ratio in which the point X (-6, h) divides the join of P (-4, 4) and Q (6, -1)

The value of 'h'

Solution:

Section formula:

If the point P(x,y) divides the join of A(x₁,y₁) and B(x₂,y₂) in the ratio m:n, then the coordinates of the point P is

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

Let the required ratio be 1: k

Then by section formula, the coordinates of the point X are

$(\frac{6+ (-4k)}{1+k} , \frac{-1+4k}{1+k})$

Since, it is given that the coordinates of the point X are (-6,h)

Comparing  the coordinates we get,

$\frac{6+ (-4k)}{1+k} = -6$ ----------------(1)

$\frac{-1+4k}{1+k} = h$ ---------------(2)

From (1) we get,

6 -4k = -6(1+k)

64k +6k = -6-6 = -12

2k = -12

k = -6

Hence the ratio in which the point divides PQ = 1:6

From equation (2) we get

$\frac{-1+4X-6}{1+-6} = h$

$h = \frac{-25}{-5} = 5$

The value of h = 5

The ratio in which the point divides PQ = 1:6

The value of h = 5

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