Question

If Q(0,1) is equidistant from P(5,_3) and (x,6), find the values of x .Also find the distances QR and PR

Answer 1

Hiii friend,


Q(0,1) , P(5,-3) and R(X,6)

It is being given that Q(0,1) is equidistant from the points P(5,-3) and R(X,6).


So we have,

QP = QR => QP² = QR²


=> (0-5)² + (1-(-3)² = (0-X)² + (1-6)²


=> (-5)² + (1+3)² = (-X)² + (-5)²

=> 25 + 16 = X²+25

=> X² = 16


=> X = ✓16 = 4


The given points are Q(0,1) and R(4,6)

Then,


X1 = 0 , Y1 = 1 and X2 = 4 , Y2 = 6


QR = ✓(X2-X1)² + (Y2-Y1)²


QR = ✓(4-0)² + (6-1)² = ✓16 + 25 = ✓31


And,


Q(0,1) and P(5,-3)

X1 = 0 , Y1 = 1 and X2 = 5 , Y2 = -3


QP= ✓(X2-X1)² + (Y2-Y1)²


QP = ✓(5-0)² + (-3-1)² = ✓25 + 16 = ✓31




HOPE IT WILL HELP YOU...... :-)

Answer 2

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