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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.

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Solution

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

The three given points are P(6,−1), Q(1,3) and R(x,8).

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,

Now we have a quadratic equation. Solving for the roots of the equation we have,

Thus the roots of the above equation are 5 and −3.

Hence the values of ‘x’ are.


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