The graphic below shows quadrilateral ABCD and its dilation, quadrilateral A’B’C’D’, with the origin as the center of dilation. The scale factor is . Which statement about both quadrilaterals is true?

Quadrilateral ABCD is congruent to quadrilateral A’B’C’D’.
The corresponding angles of quadrilaterals ABCD and A’B’C’D’ are congruent.
The corresponding sides of quadrilaterals ABCD and A’B’C’D’ are congruent.
The corresponding angles of quadrilaterals ABCD and A’B’C’D’ are not congruent.

The corresponding angles of quadrilaterals ABCD and A’B’C’D’ are congruent.

Step-by-step explanation:

One of the rules of dilation in geometry is that dilations, no matter what point you are dilating from, will change the angle. Dilations will only ever change the length of the sides.

number one is the correct answer

step-by-step explanation: dogs and cats are mentioned, no other animals

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west