1. Find a if the distance between (a, 2) and (3, 4) is 8.
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Answer:
Given:
2 points on the coordinate axis
i) (a,2)
ii) (3,4)
Distance between the given points = 8 units
To find:
Value of (a)
Formulas used:
let distance be denoted as "d"
d = √{(x2 - x1)² + (y2 - y1)²}
Calculation:
d = √{(x2 - x1)² + (y2 - y1)²}
=> 8 = √{(3 - a)² + (4 - 2)²}
=> 8 = √{(3 - a)² + 2²}
Squaring on both sides:
=> 64 = (3 - a)² + 4
=> 60 = (3 - a)²
Square root on both sides:
=> 3 - a = √60 = 7.745
=> a = 3 - 7.745 = - 4.745.
So the answer is (a = - 4.745)
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