Question

For what values of k, the points (8,1),(3,-2k) and (0,-5) are collinear?

Answer 1

If points ( 8, 1 ), ( 3, - 2k ) and ( 0, - 5 ) are collinear, then the distance between them will be equal.

Let A = ( 8, 1). B = ( 3, - 2k ), C = ( 0, - 5 )

SHOW THAT : AB + BC = AC

Using Distance formula,

D = √ ( x₁ - x₂ ) ² + ( y₁ + y₂ ) ²


AB = √ ( 8 - 3 ) ² + ( 1 + 2 k ) ²

AB = √ 25 + 1 + 4k ² + 4k

AB = √ 4k² + 4k + 26


BC = √ ( 3 - 0 )² + ( - 2k +5 )²

BC = √ 9 + 4k² +25 - 20 k

BC = √ 4k² - 20k + 34


AC = √( 8 - 0 )² +( 1+5 )²

AC = √ 64 +36

AC = √ 100

AC = 10.

=> REFER THE ATTACHMENT.

Answer 2

Answer:

Step-by-step explanation: