Question

Find the distance between
1 (2,3),(4,1)
2 (-5,7),(-1,3)
3 (a,b),(-a,-b)​

Answer 1

$\boxed{Distance \:Formula= \sqrt{{({x}_{2} - {x}_{1})}^{2} + {({y}_{2} - {y}_{1})}^{2}}}$

1. (2,3) , (4,1)

Let,

${x}_{1}, {y}_{1} = (2,3)$

${x}_{2} , {y}_{2} = (4,1)$

By using Distance Formula

$\sqrt{{(4-2)}^{2} + {(1-3)}^{2}} \\ = \sqrt{{(2)}^{2} + {(-2)}^{2}} \\ = \sqrt{4+4} \\ = 2\sqrt{2}$

2. (-5,7),(-1,3)

Let,

${x}_{1}, {y}_{1} = (-5,7)$

${x}_{2} , {y}_{2} = (-1,3)$

By using Distance Formula

$\sqrt{{(-1+5)}^{2} + {(3-7)}^{2}} \\ = \sqrt{{(4)}^{2} + {(-4)}^{2}} \\ = \sqrt{16+16} \\ = 4\sqrt{2}$

3. (a,b),(-a,-b)

Let,

${x}_{1}, {y}_{1} = (a,b)$

${x}_{2} , {y}_{2} = (-a,-b)$

By using Distance Formula

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