Q. 94.3( 3 Votes )

# If the distance between the points (3, a) and (4, 1) be then the value of a will be:

A. 3, –1

B. 2, –2

C. 4, –2

D. 5, –3

Answer :

Using the distance formula, the distance between the points (3, a) and (4, 1)

√10 =

=

=

=

Squaring both sides, we get

a^{2} – 2a +2 = 10

⇒ a^{2} – 2a – 8 = 0

⇒ a^{2} – 4a + 2a – 8 = 0

⇒ a (a – 4)+ 2 (a – 4) = 0

⇒ (a – 4) (a + 2) = 0

∴ Either a = 4 or a = –2.

∴ The correct option is **C**.

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