The distance between P(x, 7) and Q(6, 19) is 13 units. Find the values of x.
-
A.
1 or -7 -
B.
1 or 7 -
C.
1 or 11 -
D.
5 or -5
Correct Answer: Option C
Explanation
(d = sqrt{(x_{1} – x_{2})^{2} + (y_{1} – y_{2})^{2}})
(13 = sqrt{(x – 6)^{2} + (7 – 19)^{2}})
(13^{2} = x^{2} – 12x + 36 + 144)
(169 = x^{2} – 12x + 180)
(x^{2} – 12x + 180 – 169 = 0 implies x^{2} – 12x + 11 = 0)
((x – 1)(x – 11) = 0 implies x = text{1 or 11})