Question

If Q (0,1) is equidistant from P (5, −3) and R (x, 6), find the values of x. Also, find the distances QR and PR.

Answer 1

The distance d between two points and is given by the formula

The three given points are Q(0,1), P(5,−3) and R(x,6).

Now let us find the distance between ‘P’ and ‘Q’.

Now, let us find the distance between ‘Q’ and ‘R’.

It is given that both these distances are equal. So, let us equate both the above equations,

Squaring on both sides of the equation we get,

Hence the values of ‘x’ are.

Now, the required individual distances,

Hence the length of ‘QR’ is.

For ‘PR’ there are two cases. First when the value of ‘x’ is 4,

Then when the value of ‘x’ is −4,

Hence the length of ‘PR’ can beunits