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