Math Problem Statement

Find the coordinates of point C' after point C is reflected across the y-axis. In which quadrant will point C' be located?

Solution

The problem asks for the coordinates of point CC' after point CC is reflected across the y-axis. Point CC is given as (3,2)(-3, -2).

Reflection Across the y-axis:

When a point (x,y)(x, y) is reflected across the y-axis, the x-coordinate changes sign while the y-coordinate remains the same. Therefore, the coordinates of the reflected point CC' can be found using the following rule:

C(x,y)C(x,y)C'(x, y) \rightarrow C'(-x, y)

Applying this to the given point C(3,2)C(-3, -2):

C=((3),2)=(3,2)C' = (-(-3), -2) = (3, -2)

Quadrant Location:

  • Point C(3,2)C(3, -2) is in Quadrant IV, where x is positive, and y is negative.

So, the correct answer is Quadrant IV.

Would you like further details or have any other questions? Here are 5 related questions to consider:

  1. What are the rules for reflecting a point across the x-axis?
  2. How do you reflect a point across the origin?
  3. What are the coordinates of a point after being reflected across the line y=xy = x?
  4. Can you determine the distance between point CC and its reflection CC'?
  5. How do the coordinates change when reflecting a point across the line y=xy = -x?

Tip: Always pay close attention to which axis or line a point is being reflected across, as this determines how the coordinates will change.

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Math Problem Analysis

Mathematical Concepts

Geometry
Coordinate Geometry
Reflection

Formulas

Reflection across the y-axis: C'(x, y) -> C'(-x, y)

Theorems

Reflection Theorem

Suitable Grade Level

Grades 7-9