Given the triangle ABC, you have to reflect it over the y-axis and then dilate it by scale factor k=1/2
- The reflection over the y-axis is a rigid transformation (the figure changes position but it does not change shape), which means that the resulting image will be congruent to the original.
- The dilation is a nonrigid transformation, the figure changes its shape, the resulting image after dilation is similar to the original one.
Reflection over the y-axis ΔABC to ΔA'B'C'
To reflect an image over the y-axis you have to change the sign of the x-coordinate leaving the y-coordinate of each vertex equal. The rule of the reflection can be expressed as follows:
Preimage → Image
A(-1,-4) → A'(-(-1),-4)= A'(1,-4)
B(-3,-2) → B'(-(-3),-2)= B'(3,-2)
C(-1,2) → C'(-(-1),2)= C'(1,2)
After the reflection over the y-axis, the coordinates for the triangle are A'(1,-4), B'(3,-2), and C'(1,2).
ΔABC and ΔA'B'C' are congruent.
Dilation by scale factor k=1/2 ΔA'B'C' to ΔA''B''C''
To dilate a figure by a determined scale factor, you have to multiply the coordinates of each vertex by the said scale factor, you can write the dilation rule as follows:
Dilation factor k=1/2
After the dilation, the coordinates for the new triangle are A''(1/2,-2), B''(3/2,-1), and C''(1/2,1).
ΔABC and ΔA''B''C'' are similar.