Math, asked by geethaganesan420, 2 months ago

. Determine whether the given set of points are collinear or not.
(7,-2), (5,1), (3,4)​

Answers

Answered by allaramya08
0

Step-by-step explanation:

(i) collinear

(ii) collinear

(ii) non collinear

Step-by-step explanation:

Since, three points (x_1, y_1)(x

1

,y

1

) , (x_2, y_2)(x

2

,y

2

) and (x_3, y_3)(x

3

,y

3

) are called col-linear, if,

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

(i) x_1 = 7, y_1 = -2, x_2 = 5, y_2 = 1, x_3 = 3, y_3 = 4x

1

=7,y

1

=−2,x

2

=5,y

2

=1,x

3

=3,y

3

=4

Since,

7(1-4)+5(4+2) + 3(-2-1)=7(-3) + 5(6) + 3(-3) = -21 + 30 - 9 = 9 - 9=07(1−4)+5(4+2)+3(−2−1)=7(−3)+5(6)+3(−3)=−21+30−9=9−9=0

Thus,

(7,–2),(5,1) and (3,4) are col-linear.

(ii) x_1 = -2, y_1 = -8, x_2 = 2, y_2 = -3, x_3 = 6, y_3 = 2x

1

=−2,y

1

=−8,x

2

=2,y

2

=−3,x

3

=6,y

3

=2

Since,

-2(-3-2)+2(2+8) + 6(-8+3)=-2(-5) + 2(10) + 6(-5) = 10 + 20 - 30 = 30 - 30=0−2(−3−2)+2(2+8)+6(−8+3)=−2(−5)+2(10)+6(−5)=10+20−30=30−30=0

Thus,

(–2, –8), (2,–3) and (6,2) are col-linear.

(i) x_1 = a, y_1 = -2, x_2 = a, y_2 = 3, x_3 = a, y_3 = 0x

1

=a,y

1

=−2,x

2

=a,y

2

=3,x

3

=a,y

3

=0

Since,

a(3-0)+a(0+3) + a(-2-3)=3a + 3a - 2a - 3a = a\neq 0a(3−0)+a(0+3)+a(−2−3)=3a+3a−2a−3a=a

=0

Thus,

(7,–2),(5,1) and (3,4) are not col-linear.

Answered by 990kjy
1

Answer:

collinear

Step-by-step explanation:

x1= 7,y1= -2x2 = 5,y2 = 1,x3= 3,y3= 4

Since,

7(1-4)+5(4+2)+3(-2-1)= 7(-3)+5(6)+3(-3)= -21+30-9= 9-9=0

Thus,

(7,–2),(5,1) and (3,4) are col-linear.

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