Question

A points A (2, 3), B(-1, 2) and ((4, k) are collinear
Find the value of 'k'​

Answer 1

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Answer 2

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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

x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) = 0x

1

(y

2

−y

3

)+x

2

(y

3

−y

1

)+x

3

(y

1

−y

2

)=0

Where, x_1 = 2, x_2 = 4, y_1 = 3, y_2 = k, x_3 = 6, y_3 = -3x

1

=2,x

2

=4,y

1

=3,y

2

=k,x

3

=6,y

3

=−3

Substituting the values,

2(k + 3) + 4(-3 - 3) + 6(3 - k) = 02(k+3)+4(−3−3)+6(3−k)=0

2k + 6 + 4(-6) + 18 - 6k = 02k+6+4(−6)+18−6k=0

2k + 6 - 24 + 18 - 6k = 02k+6−24+18−6k=0

-4k + 0 = 0−4k+0=0

k=0k=0

Therefore, The value of k is 0.

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