Question

Prove that the distance between A(1,2) and B(3,8) be double of the distance of C( 3,-1) from the origin.

Answer 1

Distance between two points =
$\sqrt{(x _{2} - x _{1})^{2} +(y _{2} - y _{1})^{2} }$

Now Distance between A and B =
$\sqrt{(3 - 1) ^{2} + ( 8 - 2)^{2} }$

= √ 2²+6² = √4+36 = √40 = √4*10=2√10 .

Distance between C and origin =$\sqrt{ {(3 - 0)}^{2} +( - 1+ 0)^{2} }$
= √9+1 = √10

Distance between A and B = 2 ( Distance between C and origin) = 2√10 =2 * √10

Hence proved!

Answer 2

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