Math Problem Statement

What is the reflection of the point ​(4​,negative 3​) across the x​-axis? -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x y

x y graph Question content area bottom Part 1 The reflection of the point ​(4​,negative 3​) across the x​-axis is

Solution

To find the reflection of a point (x,y)(x, y) across the xx-axis:

  1. Keep the xx-coordinate unchanged.
  2. Reverse the sign of the yy-coordinate.

For the point (4,3)(4, -3):

  • The xx-coordinate remains 44.
  • The yy-coordinate changes from 3-3 to 33.

Thus, the reflection of (4,3)(4, -3) across the xx-axis is (4,3)(4, 3).

Would you like further clarification or a graphical explanation?


Related Questions:

  1. What is the reflection of the point (4,3)(4, -3) across the yy-axis?
  2. How do you find the reflection of a point across the line y=xy = x?
  3. What are the coordinates of the point (4,3)(4, -3) after a 180180^\circ rotation about the origin?
  4. What happens to a point when it is reflected across both the xx- and yy-axes?
  5. Can you generalize the reflection formula for any line y=mx+cy = mx + c?

Tip: To reflect a point across any axis or line, always consider how the coordinates relate to the line of reflection!

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Math Problem Analysis

Mathematical Concepts

Geometry
Coordinate Plane
Reflections

Formulas

Reflection across x-axis: (x, y) → (x, -y)

Theorems

Reflection properties in coordinate geometry

Suitable Grade Level

Grades 6-8