Coordinate Geometry-18

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Find the distance between the pair of points

(a) (2, 5), (1, 6); (b) (-9, -2), (4, -3); (c) (a, b), (-a, -b); (d) (a cos Θ, a sin Θ), (b cos Θ, b sin Θ)

Solution: Distance between the points (x1, y1) and (x2, y2) is given by

√[ (x1 - x2)2 + (y1 - y2)2 ]

(a) distance between (2, 5) and (1, 6)

= √[ (2 - 1)2 + (5 - 6)2 ] = √(12 + 12) = √2 units

(b) Distance between (-9, -2) and (4, -3)

= √[ (-9 - 4)2 + (-2 + 3)2 ] = √( 169 + 1) = √170 units

(c) Distance between (a, b) and (-a, -b)

= √[ (a + a)2 + (b + b)2 ] = √( 4a2 + 4a2 )

= 2 √(a2 + b2)

(d) Distance between (a cos Θ, a sinΘ) and (b cos Θ, b sin Θ)

= √[(a cos Θ - b cos Θ)2 + (a sinΘ - b sinΘ)2]

= √[ cos2 Θ (a - b)2 + sin2 Θ (a - b)2 ]

√ [ (a - b)2 (cos2 Θ + sin2 Θ)] = √ (a - b)2 units

= (a - b) units

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