Question

2. Determine whether the points are collinear
(1) A(1, -3), B(2,-5), C(-4,7) ​

Answer 1

Answer: we can get the answer by the triangle formula Thai is:-

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

Step-by-step explanation:

x1 =1

x2 = 2

x3 = -4

y1= -3

y2 -5

y3= 7

= ½ [ 1 ( 5-7 )+2(7+3 ) +(-4)(-3-5) ]

= ½ [ -2 + (2)(10)+(-4)(-8) ]

= ½ [-2+20+32]

= ½×50

= 25

25≠0

Hence the coordinates are not collinear.

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Answer 2

The given three points A(1, -3), B(2 ,- 5) and C(- 4, 7) ​ are collinear., proved.

Step-by-step explanation:

The given three points A(1, -3), B(2 ,- 5) and C(- 4, 7) ​ are collinear.

To find, the check whether the points are collinear or no t?

We know that,

The condition of three points are collinear.

$x_{1}(y_{2}-y_{3})+x_{2}(y_{3}-y_{1})+x_{3}(y_{1}-y_{2})=0$

⇒ 1( - 5 - 7) + 2(7 + 3) + (- 4)(- 3 + 5) = 0

⇒ 1( - 12) + 2(10) + (- 4)(2) = 0

⇒ - 12 + 20 - 8  = 0

⇒ 20 - 20  = 0

⇒ 0 = 0, proved.

Thus, the given three points A(1, -3), B(2 ,- 5) and C(- 4, 7) ​ are collinear., proved.