If P(2,4) is equidistant from Q(7,0) and R (X,9), find the value of X. Also find the distance PQ.

If P(2,4) is equidistant from Q(7,0) and R (X,9), find the value of X.

1.	If P(2,4) is equidistant from Q(7,0) and R (X,9), find the value of X. Also find the distance PQ.
Answer» Given: P(2,4) is equidistnat from Q(7,0) and R(X,9).then PQ = PRUsing Distance Formula :\xa0=\xa0(x2-x1)2\xa0+\xa0(y2-\xa0y1)2PQ =\xa025\xa0+\xa016\xa0\xa0=\xa041PR\xa0=\xa0(x-2)2\xa0+\xa0(5)2PQ = PR\xa0Sqauring Both Side, We get\xa0x2\xa0+ 4\xa0-4x + 25\xa0= 41=> x2\xa0- 4x -12 = 0=>\xa0x2\xa0- 6x +2x -12 = 0=> x(x-6) +2(x-6) = 0=> (x-6) (x+2) = 0=> x = -2 , 6\xa0