Question

A(k-3, k-2), B(k − 2, k − 3), and - - C(k+7, m) are 3 collinear points. Find the value of m in terms of k.​

Answer 1

Step-by-step explanation:

Given points are

$A\equiv (k-3,k-2)\: \: ; \:\: B\equiv(k-2,k-3)\:\: ;C\equiv(k+7,m)$

Since they are collinear, so their slopes will be equal

So,

$m_{AB}=m_{AC}$

$\implies \frac{(k - 3) - (k - 2)}{(k - 2) - (k - 3)} = \frac{m - (k - 2)}{(k + 7) - (k - 3)}$

$\implies \frac{(k - 3) - (k - 2)}{ - \{ (k - 3) - (k - 2) \}} = \frac{m - k + 2}{k + 7 - k + 3}$

$\implies - 1 = \frac{m - k + 2}{k + 7 - k + 3}$

$\implies - 1 = \frac{m - k + 2}{10}$

$\implies - 1 0 = m - k + 2$

$\implies m = k - 12$