Circles of Evaluation: Distance between (0, 2) and (4, 5)

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The distance between $\displaystyle x_{1}$ and $\displaystyle x_{2}$ is computed by . The distance between $\displaystyle y_{1}$ and $\displaystyle y_{2}$ is computed by line-length(y1, y2)line-length(y1, y2). Below is the equation to compute the hypotenuse of a right triangle with those amount for legs:

$\displaystyle \sqrt{line\mbox{-}length(x_{2}, x_{1})^2 + line\mbox{-}length(y_{2}, y_{1})^2}$

Suppose your player is at (0, 2) and a character is at (4, 5). What is the distance between them?

1. Identify the values of $\displaystyle x_{1}$ , $\displaystyle y_{1}$ , $\displaystyle x_{2}$ , and $\displaystyle y_{2}$

$\displaystyle x_{1}$	$\displaystyle y_{1}$	$\displaystyle x_{2}$	$\displaystyle y_{2}$
(x-value of 1st point)	(y-value of 1st point)	(x-value of 2nd point)	(y-value of 2nd point)

x_1

$\displaystyle x_{1}$

y_1

$\displaystyle y_{1}$

x_2

$\displaystyle x_{2}$

y_2

$\displaystyle y_{2}$

(x-value of 1st point)

(y-value of 1st point)

(x-value of 2nd point)

(y-value of 2nd point)

The equation to compute the distance between these points is:

$\displaystyle \sqrt{line\mbox{-}length(4, 0)^2 + line\mbox{-}length(5, 2)^2}$

2. Translate the expression above, for (0,2) and (4,5) into a Circle of Evaluation below.

Hint: In our programming language is used for $\displaystyle x^2$ and is used for $\displaystyle \sqrt{x}$

circles of distance 🖼Show image

3. Convert the Circle of Evaluation to Code below.

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