Question

find the distance between the points (a,2)(3,4) is 2√2​

Answer 1

Answer:

Values of a are 5 or 1 and distance between point (1,2) and point (3,4) or point (5,2) and point (3,4) is 2√2

Step-by-step explanation:

The distance between two points P(a,b) and Q(c,d) is calclated by following formua

$D = \sqrt{ {(a - c)}^{2} + {(b - d)}^{2} }$

Here, a = a, b = 2, c = 3, d = d and D = 2√2

now put the value of all terms in above formula

$2 \sqrt{2} = \sqrt{ {(a - 3)}^{2} + {(2 - 4)}^{2} } \\ = \sqrt{ {(a - 3)}^{2} + {( - 2)}^{2} } \\ \sqrt{ {(a - 3)}^{2} + 4 }$

Now squaring both side

${(2 \sqrt{2}) }^{2} = {( \sqrt{ {(a - 3)}^{2} + 4}) }^{2}$

$8 = {(a - 3)}^{2} + 4$

$8 - 4 = {(a - 3)}^{2}$

$4 = {( a - 3)}^{2}$

$a - 3 = + 2 \: \: or \: a - 3 = - 2 \\ a = 5 \: \: \: \: \: or \: \: a = 1$