Question

question 8 of 25

which of the following is a result of shifting a circle with equation \\((x + 3)^2 + (y - 2)^2 = 36\\) left 3 units?

a. the \\(y\\)-coordinate of the center of the circle increases by 3.
b. both the \\(x\\)- and \\(y\\)-coordinates of the center of the circle decrease by 3.
c. the \\(x\\)-coordinate of the center of the circle decreases by 3.
d. the \\(x\\)-coordinate of the center of the circle increases by 3.

Explanation:

Identify the center of the original circle

Using the Circle Equation and Standard Form of Circle knowledge points

$$
LATEXBLOCK0
$$

Apply the horizontal translation

Using the Linear Transformations knowledge point

$$
LATEXBLOCK1
$$

Analyze the change in coordinates

Using the Linear Transformations knowledge point

$$
LATEXBLOCK2
$$

Answer:

• A. The y-coordinate of the center of the circle increases by 3.
• B. Both the x- and y-coordinates of the center of the circle decrease by 3.
• C. The x-coordinate of the center of the circle decreases by 3. (Correct answer)
• D. The x-coordinate of the center of the circle increases by 3.