Question

1. Find ‘a’ if the distance of the point (4, 1) from the point (3, a) is √10.

Answer 1

a²+2a-8 = 0

a²+4a-2a-8= 0

a(a+4)-2(a+4)=0

(a+4)(a-2)=0

Either

a+4 = 0

a= -4

or

a-2 = 0

a= 2

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Answer 2

Answer:

a = 4 or -2

Step-by-step explanation:

$\sqrt{10} = \sqrt{ {(4 - 3)}^{2} + {(1 - a)}^{2} } \\ 10 = 1 + ( {1}^{2} + {a}^{2} - 2 \times 1 \times a) \\ 10 - 2 = {a}^{2} + 2 a \\ {a}^{2} + 2a - 8 = 0 \\ a = 4 \: or \: - 2$

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