Ex 7.1, 8 - Find values of y for which distance between - Ex 7.1

  1. Chapter 7 Class 10 Coordinate Geometry
  2. Serial order wise

Transcript

Ex 7.1 , 8 Find the values of y for which the distance between the points P(2, โ€“ 3) and Q(10, y) is 10 units. Let the points be P(โˆ’2, 3) & Q(10, y) Given that PQ = 10 units By distance formula PQ = โˆš((๐‘ฅ2 โˆ’๐‘ฅ1)2+(๐‘ฆ2 โˆ’๐‘ฆ1)2) x1 = 2 , y1 = โˆ’3 x2 = 10 , y2 = y PQ = โˆš(( 10 โˆ’2)2+(๐‘ฆโˆ’(โˆ’3))2) 10 = โˆš((8)2+(๐‘ฆ+3)2) Squaring both sides (10)2 = (โˆš((8)2+(๐‘ฆ+3)2))2 (10)2 = (8)2 + (y+ 3)2 100 = 64 + (y+ 3)2 100 = 64 + y2 + 32 + 2 ร— 3 ร— y 100 = 64 + y2 + 9 + 6y 0 = y2 + 6y + 64 + 9 โˆ’ 100 0 = y2 + 6y โ€“ 27 y2 + 6y โ€“ 27 = 0 y2 + 9y โ€“ 3y โ€“ 27 = 0 y(y + 9) โ€“ 3(y + 9) = 0 (y โ€“ 3) (y + 9) = 0 Hence y = 3 or y = โˆ’9 is the solution

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