InterviewSolution
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InterviewSolution
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Determine whether the points A(1, -3) , B(2,-5) and C(-4,7) are collinear or not . |
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Answer» A(1, -3) , B(2,-5) and C(-4,7) By distance formula, `d(A),(B) = sqrt((2-1)^(2)+[-5-(-3)]^(2))` `=sqrt((1)^(2) + (-5+3)^(2))` `= sqrt((1)^(2)+(-5+3))^(2))` ` =sqrt( 1+(-2)^(2))` ` = sqrt(1+4)` `= sqrt(5) `…(i) `d(B,C=)= sqrt((-4) -2)^(2) + [7-(-5)]^(2))` `= sqrt((-6)^(2) + (12)^(2))` ` = sqrt(38 + 144)` ` = sqrt(180)` ` sqrt(2xx2xx3xx3xx5)` ` = 6 sqrt(5)` ...(2) `d(A,C) = sqrt((-4-1)^(2) + [7-(-3)]^(2))` ` = sqrt((-5)^(2) + (10)^(2))` `sqrt( 25 + 100) = sqrt(125)` `sqrt(5xx5xx5xx5)` ` = 5sqrt(5)` ...(3) Adding (1) and (3) `d (A , B) + d(A,C)= sqrt(5) + 5sqrt(5) = 6 sqrt(5)` ` therefore A(A,B + d(A,C) = d (B,C)" "` ...From (2)] ...(4) `therefore ` Point A,B and C are collinear. Point A(1,-3) , (2,-5) and C(-4,7) are colliear. |
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