Assertion: The points (k - 1, k + 2), (k, k + 1) and (k + 1, k) are collinear for any value of k. Reason: Three points A, B, C are collinear if slope of AB is equal to slope of BC.

Question

Assertion: The points $(k - 1, k + 2), (k, k + 1)$ and $(k + 1, k)$ are collinear for any value of $k$ .

Reason: Three points A, B, C are collinear if slope of AB is equal to slope of BC.

Smart Achievers · Accepted Answer

(1)

$Slope of line passing through (k - 1, k + 2) and (k, k + 1) is$ $m_{1} = \frac{k + 1 - k - 2}{k - k + 1} = - 1$ $(independent of k)$

$Slope of line passing through (k, k + 1) and (k + 1, k) is$ $m_{2} = \frac{k - k - 1}{k + 1 - k} = - 1$ $(independent of k)$

$∵$ $m_{1} = m_{2}$

$∴$ $Points (k - 1, k + 2), (k, k + 1) and (k + 1, k) are collinear, for any value of k .$

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