find the value of K , if the points (7,2),(5,1) & (3,k) are collinear
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Step-by-step explanation:
The value of k is 4.
Step-by-step explanation:
Given : If the points A( 7,-2), B (5,1) and C (3,k) 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 = 7, x_2 = 5, x_3 = 3, y_1 =-2, y_2 = 1, y_3 =kx
1
=7,x
2
=5,x
3
=3,y
1
=−2,y
2
=1,y
3
=k
Substituting the values,
7(1-k) +5(k-(-2)) +3(-2-1) = 07(1−k)+5(k−(−2))+3(−2−1)=0
7-7k+5k+10-6-3=07−7k+5k+10−6−3=0
-2k+8=0−2k+8=0
2k=82k=8
k=\frac{8}{2}k=
2
8
k=4k=4
Therefore, The value of k is 4.
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