Suppose your player is at (0, 2) and a character is at (4, 5)…​

1 Identify the values of x1, y1, x2, and y2

x1 y1 x2 y2

(x-value of 1st point)

(y-value of 1st point)

(x-value of 2nd point)

(y-value of 2nd point)

What is the distance between your player and the character?

  • We can use line-length to computer the horizontal and vertical distances and then use those to find the diagonal distance.

    • The horizontal distance between x1 and x2 is computed by line-length​(​x2, x1​).

    • The vertical distance between y2 and y1 is computed by line-length​(​y2, y1​).

  • The hypotenuse of a right triangle with legs the lengths of those distances is computed by: √line-length(x2, x1)2 + line-length(y2, y1)2

  • So, when we substitute these points in, the distance between them will be computed by:

√line-length(4, 0)2 + line-length(5, 2)2

2 The points are (0,2) and (4,5). Why aren’t we using line-length​(​0, 2​) and line-length​(​4, 5​)?

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

Hint: In our programming language num-sqr is used for x2 and num-sqrt is used for √x

circles of distance

4 Convert the Circle of Evaluation to Code below.

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