If a b c are collinear points such that is equal to 3, 4 is equal to 77 and ac is equal to 10 then c is equal to
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Step-by-step explanation:
see diagram.
A (3,4) and B(7,7) and C(x,y) or C'(x,y) are collinear points.
AB = √[(7-3)²+(7-4)²] = 5
AC = 10, given.
Slope of AC = slope of AB = (7-4)/(7-3) = 3/4
=> (y-4)/(x-3) = 3/4 --- (1)
=> 4 y - 3 x = 7 --- (2)
AC² = 10² = (y - 4)² + (x - 3)²
= [ 3/4 * (x - 3) ]² + (x-3)² using (1)
= (x-3)² * 25/16
=> x - 3 = + 8
=> x = +11 or -5
=> y = (7+3x)/4 by (2)
= 10 or -2
C = (11, 10) and C' = (-5, -2)
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