Question

Shape I is similar to shape II. The sequence that proves shape I is similar to shape II when applied to shape I is a reflection across the:

(a) x-axis, followed by a translation 4 units right and 2 units down, and then a dilation by a scale factor of 0.5.
(b) y-axis, followed by a translation 5 units right and 3 units down, and then a dilation by a scale factor of 1.0.
(c) x-axis, followed by a translation 6 units right and 4 units down, and then a dilation by a scale factor of 1.5.
(d) y-axis, followed by a translation 7 units right and 5 units down, and then a dilation by a scale factor of 2.0.

Answer 1

The correct sequence that proves shape I is similar to shape II is option (c): reflection across the x-axis, followed by a translation 6 units right and 4 units down, and then a dilation by a scale factor of 1.5.

Step-by-step explanation:

The correct sequence that proves shape I is similar to shape II is option (c):

1. Reflection across the x-axis
2. Translation 6 units right and 4 units down
3. Dilation by a scale factor of 1.5

To prove that two shapes are similar, we need to apply a series of transformations that preserve their shape and size. In this case, we start with a reflection across the x-axis, followed by a translation and then a dilation. These transformations maintain the shape and size of shape I, making it similar to shape II.