1.

Find the points (3,-8);(4,-11);(5,-k) are collinear then find k​

Answer»

A(3,−8)B(4,−11)C(5,−k)

If this points are collinear

then they lie on same line  

so they will FORM a TRIANGLE  

whose AREA is O Ar.△=0

⇒  

2

1

​  

[x  

1

​  

(y  

2

​  

−y  

3

​  

)+x  

2

​  

(y  

3

​  

−y  

1

​  

)+x  

3

​  

(y  

1

​  

−y  

2

​  

)]=0  

x  

1

​  

=3   y  

1

​  

=−8

x  

2

​  

=4  y  

2

​  

=−11

x  

3

​  

=5  y  

3

​  

=−K

⇒  

2

1

​  

[3(−11+k)+4(−k−(−8))+5(−8−(−11))]=0

⇒  

2

1

​  

[3(+k−11)+4(−k+8)+5(−8+11)]=0  

⇒  

2

1

​  

[3k−33+32−4k+5(3)]=0

[−33+32+15−4k+3k]=0

[14−k]=0

k=14

k=14



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