The coordinates of triangle QRS are Q(-2, 4), R14,0) and S(6,2). The figure was dilated and the new coordinates are Q(-3, 6), R'(6,0) and S'(9,3). What is the scale factor? What is the algebraic rule?

Just take any coordinate of any point that was scaled and that had a non-zero initial value. Let’s take the x axis of Q. There’s [tex]x_Q = -2 \land x_{Q'} = -3[/tex].

So, the scaling factor has to be [tex]\frac{x_{Q'}}{x_Q} = \frac{-3}{-2} = \frac{3}{2}[/tex]. You can confirm that [tex]\frac{x_{Q'}}{x_Q} = \frac{y_{Q'}}{y_Q} = \frac{x_{R'}}{x_R} = \frac{x_{S'}}{x_S} = \frac{y_{S'}}{y_S}[/tex]. (I omitted [tex]\frac{y_{R'}}{y_R}[/tex] because of zero values)

The algebraic rule for getting the point [tex]P'(x_{P'}, y_{P'})[/tex] in the dilated space from any given point [tex]P(x_P, y_P)[/tex] is [tex]\left \{ {{x_{P'} = \frac{3}{2}x_P} \atop {y_{P'} = \frac{3}{2}y_P}} \right.[/tex]

The coordinates of triangle QRS are Q(-2, 4), R14,0) and S(6,2). The figure was dilated and the new coordinates are Q(-3, 6), R'(6,0) and S'(9,3). What is the scale factor? What is the algebraic rule?​

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The coordinates of triangle QRS are Q(-2, 4), R14,0) and S(6,2). The figure was dilated and the new coordinates are Q(-3, 6), R'(6,0) and S'(9,3). What is the scale factor? What is the algebraic rule?