Reflect figures across the x-axis

Reflection across the x-axis maps each point $(x, y)$ to $(x, -y)$ : the x-coordinate remains unchanged, while the y-coordinate changes sign, so points above and below the axis are equal distances from it. The image preserves lengths, angle measures, and shape, with points on the x-axis fixed; this distinguishes the transformation from changing the x-coordinate and supports reasoning about congruence and coordinate rules.

Detailed Explanation: Reflect figures across the x-axis

To reflect a figure across the $x$ -axis, keep each $x$ -coordinate the same and change the sign of each $y$ -coordinate.

The rule is:

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

A point above the $x$ -axis moves the same distance below it.
A point below the $x$ -axis moves the same distance above it.
A point on the $x$ -axis stays in the same place.

Example

Reflect triangle $(ABC)$ across the $x$ -axis.

A(2,4),\qquad B(5,1),\qquad C(-3,-2)

Apply the rule to each point:

Point $(A(2,4))$ :

(2,4)\rightarrow(2,-4)

So, $(A'=(2,-4))$ .

Point $(B(5,1))$ :

(5,1)\rightarrow(5,-1)

So, $(B'=(5,-1))$ .

Point $(C(-3,-2))$ :

(-3,-2)\rightarrow(-3,2)

So, $(C'=(-3,2))$ .

The reflected triangle has vertices

\boxed{A'(2,-4),\quad B'(5,-1),\quad C'(-3,2)}

Notice that the $x$ -coordinates stayed the same, while each $y$ -coordinate changed sign. Plot the new points and connect them in the same order to draw the reflected figure.

Learn by doing: Reflect figures across the x-axis

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Cartesian Grid - Reflection of Point (Coordinates to Coordinates) across Axis

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