Find the value of t, if the distance between the points P...
Find the value of t, if the distance between the points P(–3, –14) and Q(t, –5) is 9 units.
3
2
-3
-2
Correct answer is C
Let the given points be:
P(-3, -14) = (x1, y1)
Q(t, -5) = (x2, y2)
PQ = 9 units (given)
Using the distance formula,
d = √ [ (x2−x1)2+(y2−y1)2]
PQ = √ [ (t−(−3))2+(−5+14)2]
⟹ √ [ (t+3)2+81] = 9
Squaring on both sides,
⇒ (t + 3)2 + 81 = 81
⇒ (t + 3)2 = 0
⇒ t + 3 = 0
∴ t = -3