Find the values of x for which the distance between the points P(x, 4) and Q(9, 10) is 10 units.
Given the distance PQ = 10 units
By distance formula, as shown below:
PQ = √{(9 – x)2 + (10 – 4)2}
10 = √{(9 – x)2 + (6)2}
10 = √{81 + x2 – 18x + 36}
10 = √{117 + x2 – 18x}
Squaring both sides we get
⇒ 100 = 117 + x2 – 18x
⇒ x2 – 18x + 17x = 0
⇒ (x – 1)(x – 17)
⇒ × = 1 or × = 17
6