Question

Find the distance between the following points 1.A(2,0) and B(0,4) 2.P (0,5) and Q (12,0)

Answer 1

Answer:-

$\huge \: distance \: formula = \sqrt{ ({x_2 - x_1})^{2} + {(y_2 - y_1})^{2} }$

$1)given : - \\x_1 = 2 \\ y_1 = 0 \\ x_2 = 0 \\ y_2 = 4 \\ substitute \: \: in \: formula \\ = \sqrt{(0 - 2) ^{2} + {(4 - 0)}^{2} } \\ = \sqrt{ {( - 2)}^{2} + {(4)}^{2} } \\ = \sqrt{4 + 16 } \\ = \sqrt{20} \\ = 2 \sqrt{5} \\ 2)given : - \\ x_1 = 0 \\ y_1 = 5 \\ x_2 = 12 \\ y_2 = 0 \\ substitute \: in \: formula \: \\ = \sqrt{ {(12 - 0)}^{2} + {(0 - 5)}^{2} } \\ = \sqrt{ {(12)}^{2} + {( - 5)}^{2} } \\ = \sqrt{144 + 25} \\ = \sqrt{169} \\ = 13$