Question

Which of the following transformations to ∆ABC would NOT preserve size and shape?

a) Translation of (x – 5, y + 2)
b) Reflection over the x-axis
c) Dilation of scale factor 2
d) Rotation 90° clockwise

Answer 1

Dilation with a scale factor of 2 does not preserve the size and shape of a triangle, unlike translation, reflection, and rotation, which are rigid motions that maintain the figure's geometry.

Step-by-step explanation:

The transformation that would NOT preserve the size and shape of ∆ABC is a dilation with a scale factor of 2. This is because a dilation changes the size of the figure, while translation, reflection, and rotation do not alter the size or shape of a figure.

• Translation of (x – 5, y + 2) simply slides the triangle to a different position without changing its size or shape.
• Reflection over the x-axis flips the triangle over the x-axis, producing a mirror image, yet preserves the size and shape.
• Dilation of scale factor 2 enlarges the triangle, thus changing its size.
• Rotation 90° clockwise turns the triangle around a point (usually the origin), preserving its size and shape.

In summary, while translation, reflection, and rotation are rigid motions that maintain the integrity of the geometry of the figure, dilation is not a rigid motion and will alter the size, thereby not preserving the original size and shape of ∆ABC.