First slide

Cartesian plane

Question

The points (2, 1), (8, 5) and (k, 7) lie on a straight line. Then the values of k is

Moderate

A

10
B

11
C

13
D

12

Solution

$A (2, 1), B (8, 5), C (k_{1} 7)$ lie on a straight line $\Rightarrow Δ A B C = 0$
$\Rightarrow \frac{1}{2} | \begin{matrix} - 6 & - 4 \\ 2 - k & - 6 \end{matrix} | = 0 \Rightarrow$ $| - 4 k + 44 | = 0 \Rightarrow k = 11$

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