Question

for what value of "k" are the point (8,1) (k,-4) and (2,-5) collinear

Answer 1

My handwriting might disturb you

Answer 2

hey dear

here is your answer

to find K points are ( 8,1) , (k,-4) , (2,-5) are collinear

So the solution started below

A, B, C are the collinear points

Area of triangle A, B, C is 0

so there

area of triangle can be founded by the formula

so the formula is

1/2, x1(y2-y3) +x2(y3-y1) +x3( y1-y2)

x1,x2,x3, y1,y2,y3

using this formula we can find value of K

So. (1/2 is 0 )

1/2 , 8(-4 -(-5) ) K ( -5 +(-1) ) 2( 1 -(-4) )

so we solve this simply

0= 8( -4+5) K ( -5-1) 2( 1+4)

0= 8 (1) K (-6) 2( 5)

8 -6k + 10 =0

-6k +18 = 0

transpose 18 from RHS to LHS

-6k = -18

so, -6 comes into divide

K = -18/-6

So K value comes =3

Answer is 3

hope it helps

thank you