Coordinate Reflection of Triangle ΔEFG Across the X-Axis

Math Problem Statement

Show how each vertex of ΔEFG maps to its image. Describe in words how to map ΔEFG to its image ΔE'F'G' using a reflection. Complete the table with the coordinates of the image points E', F', and G'.

Solution

The task involves mapping triangle $\Delta EFG$ to its reflection, triangle $\Delta E'F'G'$ , and completing the coordinates of points $E'$ , $F'$ , and $G'$ .

Analyzing the Reflection:

The reflection appears to be across the x-axis, based on the positioning of the original triangle $\Delta EFG$ and its reflected image $\Delta E'F'G'$ .

For a reflection across the x-axis, the coordinates of any point $(x, y)$ change to $(x, -y)$ . This transformation applies to all the vertices $E$ , $F$ , and $G$ .

Step-by-Step Reflection:

$E(-3, 5)$ reflects to $E'(-3, -5)$ .
$F(-2, 2)$ reflects to $F'(-2, -2)$ .
$G(-4, 2)$ reflects to $G'(-4, -2)$ .

Completing the Table:

\hline \Delta EFG & \Delta E'F'G' \\ \hline E(-3, 5) & E'(-3, -5) \\ F(-2, 2) & F'(-2, -2) \\ G(-4, 2) & G'(-4, -2) \\ \hline \end{array}$$ Would you like further details or have any questions? ### Related Questions: 1. What is the general rule for reflecting a point across the y-axis? 2. How would the reflection change if the triangle were reflected across the y-axis instead? 3. What happens to the coordinates of a point when reflected across the line $$y = x$$? 4. Can you determine the distance between the original points and their reflections? 5. How can you verify if two triangles are congruent after a reflection? ### Tip: Always remember that reflecting a point across the x-axis only changes the sign of the y-coordinate.

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Math Problem Analysis

Mathematical Concepts

Geometry
Coordinate Reflections
Transformations

Formulas

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

Theorems

Reflection Theorem across the x-axis

Suitable Grade Level

Grades 6-8

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