graph the image of rectangle stuv after a reflection over the x - axis.
graph the image of rectangle stuv after a reflection over the x - axis.
Answer
Explanation:
Step1: Recall reflection rule
The rule for reflecting a point $(x,y)$ over the $x -$axis is $(x,-y)$.
Step2: Identify rectangle vertices
Let's assume the vertices of rectangle $STUV$ have coordinates $S(x_1,y_1)$, $T(x_2,y_2)$, $U(x_3,y_3)$, $V(x_4,y_4)$.
Step3: Apply reflection rule
The new vertices after reflection over the $x -$axis will be $S'(x_1,-y_1)$, $T'(x_2,-y_2)$, $U'(x_3,-y_3)$, $V'(x_4,-y_4)$.
Step4: Plot new rectangle
Plot the points $S'$, $T'$, $U'$, $V'$ on the coordinate - grid and connect them to form the reflected rectangle.
Since no specific coordinates are given for the vertices of rectangle $STUV$ in the problem statement, the general procedure for graphing the reflection over the $x -$axis is as described above. If we assume for example that $S(- 6,-9)$, $T(-2,-9)$, $U(-2,-5)$, $V(-6,-5)$:
- For point $S(-6,-9)$, after reflection over the $x -$axis, $S'(-6,9)$.
- For point $T(-2,-9)$, after reflection over the $x -$axis, $T'(-2,9)$.
- For point $U(-2,-5)$, after reflection over the $x -$axis, $U'(-2,5)$.
- For point $V(-6,-5)$, after reflection over the $x -$axis, $V'(-6,5)$. Then we plot these new points $S'$, $T'$, $U'$, $V'$ and connect them to get the reflected rectangle.
Answer:
Plot the new rectangle with vertices obtained by applying the rule $(x,y)\to(x, - y)$ to the original rectangle's vertices.