# If the distance between the points (3, a) and (4, 1) be then the value of a will be:A. 3, –1B. 2, –2C. 4, –2D. 5, –3

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

√10 =

=

=

=

Squaring both sides, we get

a2 – 2a +2 = 10

a2 – 2a – 8 = 0

a2 – 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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