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Question
Show that points A(–1, –1), B(0, 1), C(1, 3) are collinear.
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Solution 1
A(–1, –1), B(0, 1), C(1, 3)
AB = `sqrt((0 + 1)^2 + (1 + 1)^2`
= `sqrt(1 + 4)`
AB = `sqrt(5)`
BC = `sqrt((1)^2 + (2)^2`
= `sqrt(1 + 4)`
BC = `sqrt(5)`
AC = `sqrt((2)^2 + (3 + 1)^2`
= `sqrt(4 + 16)`
= `sqrt(20)`
= `sqrt(5 xx 4)`
AC = `2sqrt(5)`
AB + BC = AC
`sqrt(5) + sqrt(5) = 2sqrt(5)`
A, B, and C are collinear.
Solution 2
A`(x_1, y_1) = (-1, -1)`
B`(x_2, y_2) = (0,1)`
C`(x_3, y_3) = (1, 3)`
Slope of line
AB = `(y_2 - y_1)/(x_2 - x_1)`
= `(1 - (-1))/(0 - (-1))`
= `(1+1)/1 = 2`
Slope of line
BC = `(y_3 - y_2)/(x_3 - x_2)`
= `(3 - 1)/(1 - 0)`
= `2/1 = 2.`
As, slope of line AB = slope of line BC
Also AB and BC Hrtes contain common point B
∴ Points A, B, C are collinear. Hence Proved
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Tharunya was thrilled to know that the football tournament is fixed with a monthly timeframe from 20th July to 20th August 2023 and for the first time in the FIFA Women’s World Cup’s history, two nations host in 10 venues. Her father felt that the game can be better understood if the position of players is represented as points on a coordinate plane. |
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[or]
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