Question

4. A dilation of (x,y) → (kx, ky) when 0 <k< 1 has what effect on the figure?

What is the effect on the figure when k > 1?​

Answer 1

Dilation with 0 < k < 1 causes a figure to shrink (contraction), while dilation with k > 1 causes a figure to enlarge (expansion). The shape remains unchanged, but the size adjusts based on the value of k.

Step-by-step explanation:

A dilation is a transformation that stretches or compresses a figure proportionally from a centre point. When a figure undergoes a dilation given by the transformation (x, y) → (kx, ky), the ratio k determines the nature of the dilation.

• If 0 < k < 1, the figure scales down, meaning it shrinks. Each point is moved closer to the centre of dilation, which reduces the size of the figure. This is called a contraction.
• When k > 1, the figure scales up, which causes it to enlarge. Each point moves away from the centre, increasing the distances proportionally, leading to an expansion of the figure.

By varying the value of k, you can control the size of the image after the dilation. It’s important to note that the shape of the figure does not change; only its size does.

Answer 2

It depends on what your k is equal to let me know