 Hi and welcome to the session. Let's work out the following question The question says find the value of x such that pq is equal to qr where the coordinates of pq and rr 6 minus 1, 1, 3 and x8 respectively Let's start with the solution to this question First of all, let the point p equal to 6 minus 1 that is given to us in the question q is 1, 3 and r is x8 therefore pq is equal to square root of 1 minus 6 the whole square plus 3 minus minus 1 the whole square that is equal to square root of minus 5 the whole square plus 4 square this happens because distance between two points x1, y1 and x2, y2 is given by square root of x2 minus x1 the whole square plus y2 minus y1 the whole square This is same as square root of 25 plus 16 and that is equal to square root of 41 and also qr is equal to square root of x minus 1 the whole square plus 8 minus 3 the whole square That is equal to square root of x minus 1 the whole square plus 5 square That is equal to square root of x minus 1 the whole square plus 25 This is given to us in the question that pq is equal to qr, therefore square root of 41 is equal to square root of x minus 1 the whole square plus 25. Now taking squares on both the sides we have 41 is equal to x minus 1 the whole square plus 25 or 41 minus 25 is equal to x minus 1 the whole square or 16 is equal to x minus 1 the whole square. This would imply that x minus 1 is equal to plus minus square root of 16 or x minus 1 is equal to plus minus 4. So we have either x is equal to 4 plus 1 or x is equal to minus 4 plus 1 here x will be equal to 5 and here x will be equal to minus 3. So our answer to this question is x is equal to 5 or minus 3. I hope that you understood the solution and enjoyed the session. Have a good day.