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Math  /  Geometry

QuestionWhat is the image of (−4,−2)(-4,-2) after a reflection over the xx-axis?

Studdy Solution

STEP 1

What is this asking? Where does the point (−4,−2)(-4, -2) end up after we flip it over the x-axis? Watch out! Don't flip over the wrong axis!
The *x*-axis is the horizontal one.

STEP 2

1. Visualize the reflection
2. Determine the coordinates

STEP 3

Imagine the *x*-axis as a mirror.
Our point (−4,−2)(-4, -2) is **below** the *x*-axis.
When we look in the mirror, where will we see its reflection?

STEP 4

It'll be on the **opposite side** of the *x*-axis, but the same distance away.
Think of folding a piece of paper along the *x*-axis – where would (−4,−2)(-4, -2) land?

STEP 5

Our **original point** is (−4,−2)(-4, -2).
The *x*-coordinate tells us how far **left or right** the point is from the center.
The *y*-coordinate tells us how far **up or down** it is.

STEP 6

When we reflect over the *x*-axis, we're essentially flipping the point vertically.
So, the *x*-coordinate stays the **same**.
The *y*-coordinate, however, changes its **sign**.

STEP 7

Our **original *x*-coordinate** is −4-4.
This stays the same after the reflection.

STEP 8

Our **original *y*-coordinate** is −2-2.
After the reflection, it becomes its opposite, which is +2+2.
We can think of this as multiplying −2-2 by −1-1: (−1)⋅(−2)=2 (-1) \cdot (-2) = 2

STEP 9

So, our **new point** has an *x*-coordinate of −4-4 and a *y*-coordinate of 22.
That's (−4,2)(-4, 2)!

STEP 10

The image of (−4,−2)(-4, -2) after a reflection over the *x*-axis is (−4,2)(-4, 2).

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