Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Mar 13, 2024

Find the point symmetric to (5,-4) w.r.t. $x$ -axis, $y$ -axis, and origin. The point symmetric to (5,-4) w.r.t. $x$ -axis is $(5,4)$ .

STEP 1

Assumptions
1. The given point is $(5, -4)$ .
2. Symmetry with respect to the $x$ -axis involves flipping the point over the $x$ -axis, which changes the sign of the $y$ -coordinate.
3. Symmetry with respect to the $y$ -axis involves flipping the point over the $y$ -axis, which changes the sign of the $x$ -coordinate.
4. Symmetry with respect to the origin involves flipping the point over both axes, which changes the signs of both coordinates.

STEP 2

To find the point symmetric to $(5, -4)$ with respect to the $x$ -axis, we only change the sign of the $y$ -coordinate.
$Symmetric\, point\, (x-axis) = (x, -y)$

STEP 3

Plug in the values for $x$ and $y$ from the given point $(5, -4)$ to find the symmetric point with respect to the $x$ -axis.
$Symmetric\, point\, (x-axis) = (5, -(-4))$

STEP 4

Calculate the symmetric point with respect to the $x$ -axis.
$Symmetric\, point\, (x-axis) = (5, 4)$
The point symmetric to $(5, -4)$ with respect to the $x$ -axis is $(5, 4)$ .

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