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Question: If the points \(A(3,\ 4),B(7,\ 7),C(a,\ b)\) be collinear and \(AC = 10\), then \((a,\ b)\) =...

If the points A(3, 4),B(7, 7),C(a, b)A(3,\ 4),B(7,\ 7),C(a,\ b) be collinear and AC=10AC = 10, then (a, b)(a,\ b) =

A

(11, 10)(11,\ 10)

B

(10, 11)(10,\ 11)

C

(11/2,5)(11/2,5)

D

(5, 11/2)(5,\ 11/2)

Answer

(11, 10)(11,\ 10)

Explanation

Solution

(a−3)2+(b−4)2=100( a - 3 ) ^ { 2 } + ( b - 4 ) ^ { 2 } = 100 and b−73=a−74\frac { b - 7 } { 3 } = \frac { a - 7 } { 4 }

Hence (a, b)=(11, 10).

Trick : Check with options. We find that the
point (11, 10) satisfies both the conditions i.e.

AC=(11−3)2+(10−4)2=10A C = \sqrt { ( 11 - 3 ) ^ { 2 } + ( 10 - 4 ) ^ { 2 } } = 10. Also this is collinear

with A, B.