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Geometry: Double reflection: Angle between the degrees is half the angle of rotation regardless of the order of reflection?

Bymchammmmmmmmeer

Hello, My question relates to the following situation: First the red triangle is created and then the green one, by reflection. However, all proofs regarding the angle of degrees as half an angle of rotation refer to congruence mappings where multiple reflections represent the rotation in ONE direction and not with an outward (counterclockwise (blue…

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Hamburger02
Hamburger02
10 months ago

What you need to know by heart:

If two straight lines are perpendicular to each other, the two slopes are:

m2 = -1

This can be solved according to m2:
m2 = -1/ m1
with m1= gradient of f(x) = -1/3 follows from this:
m2 = -1 / -(1/3) = -1 * -3 = 3

Therefore, the approach for h(x):
h(x) = 3x + b

b we get out with P(1/5):
5 = 3 * 1 + b
b = 5 – 3 = 2

This is the solution:
h(x) = 3x + 2

This looks like a graph:

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Tannibi
Tannibi
10 months ago

Orthogonal means vertical. If a straight line h(x) is perpendicular
to f(x) and f(x) has the slope m, h(x) has the slope -1/m.

Now you have the gradient of the sought straight lines and a
Point is given, you can determine the straight line equation.

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