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Question

If P,Q,R are (6,1),(1,3),(x,8) respectively, then find the value of x so that PQ=QR

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Solution

Distance between two points=(x2x1)2+(y2y1)2

Given:PQ=QR

(16)2+(3+1)2=(x1)2+(83)2

(5)2+(4)2=(x1)2+(5)2

25+16=x22x+1+25

41=x22x+26

squaring both sides, we get

x22x+2641=0

x22x15=0

x2+3x5x15=0

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

(x+3)(x5)=0

x=3,5

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