G.6.3.1 Why is it a Dilation?

Point B was transformed using the coordinate rule (x, y)[math]\longrightarrow[/math](3x, 3y).
Add these auxiliary points and lines to create 2 right triangles: Label the origin P. Plot points M = (2, 0) and N = (6, 0). Draw segments PB', MB, and NB'.
How do triangles PMB and PNB' compare? How do you know?
The definition of a dilation is: [br]With scale factor k, a dilation takes a point k times farther away from the center of dilation.[br][br]How does this match what’s happening the coordinate rule (x, y)[math]\longrightarrow[/math](3x, 3y)?
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– Katie Akesson

Information: G.6.3.1 Why is it a Dilation?