Question

If the distance between P(a, -1) and Q (5, 3) is 5 units, then a = _______.

• A. -8 or -2
• B. 8 or 2
• C. 8 or -2
• D. -8 or 2

Answer 1

The correct option is B

8 or 2

PQ = 5 units (given)

$P{Q}^2=5^2$

$(a-5{)}^2+(-1-3{)}^2=5^2$

$(a-5{)}^2=5^2-4^2$

$(a-5{)}^2=3^2$ (Pythagoras Triplets 3 - 4 -5)

a-5 = 3 or a-5 = -3

a = 8 or a = 2