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Question
Find the value of a, if the distance between the points A(–3, –14) and B(a, –5) is 9 units.
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Solution
Distance between two points (x1, y1) ( x2, y2) is:
d = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
Distance between A(–3, –14) and B(a, –5) is:
d = `sqrt([(a + 3)^2 + (-5 + 14)^2])` = 9
Squaring on L.H.S and R.H.S.
(a + 3)2 + 81 = 81
(a + 3)2 = 0
(a + 3)(a + 3) = 0
a + 3 = 0
a = –3
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