Question

2. Find the value of 'K' if the points A(2,3), B(4,K) and C(6,-3) are collinear.​

Answer 1

Answer:

The value of k is 0.

Step-by-step explanation:

Given : If the points A( 2,3), B (4,k) and C (6,-3) are collinear.

To Find : The value of k?

Solution :

When three points are collinear then the condition is

$x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2) = 0$

WHERE,

$x1 = 2 \: x2 = 4 \: y1 = 3 \: y2 = k \: x3 = 6 \: y3 = - 3$

Substituting the values,

$2(k + 3) + 4( - 3 - 3) + 6(3 - k) = 0 \\ 2k + 6 + 4( - 6) + 18 - 6k = 0 \\ 2k + 6 - 24 + 18 - 6k = 0 \\ - 4k + 0 = 0 \\ k = 0$

Therefore, The value of k is 0.

Answer 2

Answer:

k = 0

Step-by-step explanation:

w.k.t,

if three points are collinear , area of triangle formed by these points is 0 .

so,

1/2 | x¹(y² - y³) + x² (y³ - y¹) + x³ (y¹ - y² ) | =0

1/2 | 2(k + 3 ) + 4 (-3-3 ) +6 (3- k ) | =0

1/2 | 2k + 6 -24 +18 -6k | = 0

1/2 |- 4k | = 0

4 k = 0

k = 0

Hope it helps you dear!!!!

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