Question

find the value of k if points (1,2) (3,4/3) and (k, - 4) are collinear​

Answer 1

hope you will find this helpful..

Answer 2

Step-by-step explanation:

Given: $(1,2),\:(3, \frac{4}{3} ) \: and \: (k, - 4)$

To find: Value of k if given points are collinear.

Solution:

Tip:

If points are collinear than area of triangle formed by joining these points are zero, because we can't make a triangle with collinear points.

Area of triangle=

$\frac{1}{2} \left |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)\right |$

Step 1: Put the points into the formula

$= \frac{1}{2} \left |1( \frac{4}{3} + 4) + 3( - 4 - 2) + k(2 - \frac{4}{3} )\right |$

Step 2: Take LCM and simplify

$\left |1\left ( \frac{4 + 12}{3}\right ) + 3( - 6) + k\left (\frac{6 - 4}{3}\right )\right | = 0$

$\left |\frac{16}{3} - 18 + \frac{2k}{3} \right | = 0$

or

$|16 - 54 + 2k| = 0$

$| - 38 + 2k| = 0$

$2k = 38$

$k = \frac{38}{2}$

$\bf k = 19$

Final answer:

Value of k is 19.

Hope it helps you.

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