Question

Find the value of x such that PQ=QR where the coordinates of P, Q and R are (6,-1), (1, 3) and (x, 8) respectively.

Answer 1

Answer:

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Answer 2

Given:

PQ=QR

coordinates of P, Q and R are (6,-1), (1, 3) and (x, 8)

Solution:

PQ = QR

Therefore, PQ² = QR²

=> (6-1)² + (-1-3)² = (x-1)² + ( 8-3)²

=> 5² + (-4)² = (x-1)² + 5²

=> 25+16 = x²-2x+1 + 25

=> 41 =  x²-2x + 26

=> x² -2x +26-41 = 0

=> x²-2x-15 =0

=> x²-5x+3x-15=0

=>x ( x-5) + 3 ( x-5) = 0

=> (x+3) (x-5) = 0

x = -3  or x =5