Question

Square ABCD is shown in the xy-coordinate plane. The square will be

dilated with the center O by a scale factor of 2 to create square A'B'C'D'.
Which statements are true?
Select all that apply.

BC ||B'C'
AC=A'C'
AD_CD
Point D' has the same coordinates as point C.
Point C' lies on the line containing points 0 and C.

Answer 1

Statements 1 and 5 are true.

Step-by-step explanation:

To determine which statements are true, let's analyze each option:

1. BC || B'C': This statement is true. When a figure is dilated by a scale factor of 2, all the sides of the figure are parallel to the corresponding sides of the original figure.
2. AC = A'C': This statement is not necessarily true. The lengths of corresponding sides of a dilated figure are not always equal.
3. AD > CD: This statement is false. In a dilated figure, the ratio of corresponding sides remains the same. So, if AD is equal to CD in the original square, it will also be equal in the dilated square.
4. Point D' has the same coordinates as point C: This statement is false. When a figure is dilated, the coordinates of its vertices change according to the scale factor and the center of dilation.
5. Point C' lies on the line containing points O and C: This statement is true. When a figure is dilated, the line connecting the center of dilation to a vertex passes through the corresponding vertex of the dilated figure.

In summary, statements 1 and 5 are true.

Answer 2

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Answer:

A, C, D, E

Step-by-step explanation:

Dilation does not change angles or directions. Every image point X' lies on the line containing the center of dilation and the pre-image point X. If the scale factor is other than 1, no image segment will be congruent to its pre-image segment. So, the following are true:

• BC║B'C'
• AC ⊥ line C'D'
• D' and C have the same coordinates
• C' lies on line OC