Question

(a,-1) and (5,3) is 5 units

Answer 1

Let A(x1,y1)=(a,-1),

B(x2,y2) = (5,3)

Distance between joining the two points A and B = 5 units

AB = 5 units

On Squaring both sides,we get

AB² = 25

=> (x2-x1)²+(y2-y1)² = 25

=> (5-a)²+[3-(-1)]² = 25

=> (5-a)² + (3+1)² = 25

=> (5-a)² + 4² = 25

=> (5-a)² = 25-16

=> (5-a)² = 9

=> 5-a = ±√9

=> 5-a = ±3

=> -a = -5±3

Therefore,

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

=> -a = -2 or -a = -8

=> a = 2 or a = 8

••••

Answer 2

$given \: question \: is - - \\ \sqrt{(a - 5) {}^{2} + (3 - ( - 1)) {}^{2} } = 5 \\ (a - 5) {}^{2} + 16 = 25 \\ a {}^{2} + 25 - 10a = 9 \\ a {}^{2} - 10a +16 \\ = a {}^{2} - 8a - 2a + 16 = 0 \\ a(a - 8) - 2(a - 8) = 0 \\ a = 8 \: or2$

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