Math  /  Geometry

QuestionDraw the reflection of the quadrilateral across the xx-axis.

Studdy Solution

STEP 1

What is this asking? Flip this quadrilateral over the horizontal line! Watch out! Make sure you flip it over the correct axis, the *x*-axis, not the *y*-axis!

STEP 2

1. Understand Reflections
2. Find Reflected Points
3. Draw the Reflected Quadrilateral

STEP 3

Imagine folding a piece of paper along the x\text{x}-axis.
A reflection across the x\text{x}-axis is like creating a mirror image of the shape on the other side of that fold.

STEP 4

When we reflect a point across the x\text{x}-axis, its x\text{x}-coordinate stays the **same**, but its y\text{y}-coordinate becomes the **opposite**.
So, if a point is at (x,y)(\text{x}, \text{y}), its reflection will be at (x,y)(\text{x}, -\text{y}).

STEP 5

Let's look at our quadrilateral.
It has four vertices.
Let's call them A, B, C, and D.
We'll estimate their coordinates.
Point A is approximately at (3,3)(\textbf{3}, \textbf{3}).
Point B is approximately at (5,4)(\textbf{5}, \textbf{4}).
Point C is approximately at (6,7)(\textbf{6}, \textbf{7}).
And Point D is approximately at (8,5)(\textbf{8}, \textbf{5}).

STEP 6

Now, let's find the reflected points!
For point A (3,3)(\textbf{3}, \textbf{3}), the reflected point, A', will be at (3,-3)(\textbf{3}, \textbf{-3}).
We kept the x\text{x}-coordinate the same and took the opposite of the y\text{y}-coordinate.

STEP 7

For point B (5,4)(\textbf{5}, \textbf{4}), the reflected point, B', will be at (5,-4)(\textbf{5}, \textbf{-4}).

STEP 8

For point C (6,7)(\textbf{6}, \textbf{7}), the reflected point, C', will be at (6,-7)(\textbf{6}, \textbf{-7}).

STEP 9

For point D (8,5)(\textbf{8}, \textbf{5}), the reflected point, D', will be at (8,-5)(\textbf{8}, \textbf{-5}).

STEP 10

Now that we have the coordinates of the reflected points, we can draw the reflected quadrilateral!
We connect A' to B', B' to C', C' to D', and D' back to A'.
And there you have it!
The reflected quadrilateral sits perfectly below the x\text{x}-axis, just like a mirror image.

STEP 11

The reflected quadrilateral has vertices at approximately (3,-3)(\textbf{3}, \textbf{-3}), (5,-4)(\textbf{5}, \textbf{-4}), (6,-7)(\textbf{6}, \textbf{-7}), and (8,-5)(\textbf{8}, \textbf{-5}).

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