8 pointed star graph

Geometry Level 3

Four sets of pairs of parallel lines are graphed. Each line shares an x-intercept with one other line and a y-intercept with one other line.

The lines appear to show an 8-pointed star.

If the star has 8 fold rotational symmetry and all 8 points of the star are equal size, give the slope of the blue line.

The answer is 2.414213562.

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1 solution

David Vreken
Jan 7, 2019

Since the star has 8 8 -fold rotational symmetry, the center is a regular octagon with interior angles of 135 ° 135° . The angle θ \theta between the blue line and the x x -axis is half this angle, so θ = 135 ° 2 \theta = \frac{135°}{2} , and since m = tan θ m = \tan \theta , the slope m m of the blue line is is m = tan 135 ° 2 = 2 + 1 2.414213562 m = \tan \frac{135°}{2} = \sqrt{2} + 1 \approx \boxed{2.414213562} .

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