Question

Find the value of k if the line x + y + k = 0 divides the line segment joining, p(4, 4) and Q (7, 7) in the ratio 5 : 8 externally

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Answer 1

We will first find the point of intersection R.

We will substitute the co-ordinates of R in x + y + k = 0 to find the value of k.

The ratio is 5 : -8.

$\Rightarrow R\equiv (\frac{5x7-8x4}{5-8},\frac{5x7-8x4}{5-8})$

$\equiv (-1,-1)$

Substituting in the given equation

x + y + k = 0

$\Rightarrow$ - 1 - 1 + k = 0

$\Rightarrow$ k = 2