Question

Find all possible values of a when the distance between. 2) (a, -1) and (5, 3) is 5 units​

Answer 1

Step-by-step explanation:

Using distance formula,

$\sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} }$

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

Using the identity,

${(a - b)}^{2} = {a}^{2} - 2ab + {b}^{2}$

$\sqrt{ {(25 - 10a + {a}^{2} )}+ {(4)}^{2} } = 5$

Squaring both sides,

$\not25 - 10a + {a}^{2} + 16 = \not25$

${a}^{2} - 10a + 16 = 0$

${a}^{2} - 8a - 2a + 16 = 0$

$a(a - 8) - 2(a - 8) = 0$

$(a - 2)(a - 8) = 0$

$a = 2 \: \: \: \: \: \: \: \: \: or \: \: \: \: \: \: \: a = 8$

Hence the value of "a" is either 2 or either 8