What is the distance between $(2, 6)$ $(2,6)$ and $(4, 4)$ $(4,4)$ ?

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Answer 1 · 2015-11-26T16:54:16

$2 \sqrt{2}$ $2sqrt(2)$

Consider these point as forming a triangle. You can then use Pythagoras to solve the length of the hypotenuse (the line between the points.

Let the distance be d

Let $(x_{1}, y_{1}) \to (2, 6)$ $(x_1,y_1) -> (2,6)$
Let $(x_{2}, y_{2}) \to (4, 4)$ $(x_2,y_2)->(4,4)$

Then
$d = \sqrt{{(x_{2} - x_{1})}_{2}^{2} + {(y_{2} - y_{1})}_{2}^{2}}$ $d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)$

$d = \sqrt{{(4 - 2)}^{2} + {(4 - 6)}^{2}}$ $d=sqrt((4-2)^2+(4-6)^2)$

$d = \sqrt{2^{2} + {(- 2)}^{2}}$ $d=sqrt(2^2+(-2)^2)$

$d = \sqrt{8} = \sqrt{2 \times 2^{2}}$ $d=sqrt(8) = sqrt(2xx2^2)$

$d = 2 \sqrt{2}$ $d=2sqrt(2)$

By keeping the square root you have an exact solution.
If you tried using decimal it would not be!

What is the distance between (2,6)(2,6) and (4,4)(4,4)?