Question

draw the image of the rotation of quadrilateral sort by 270° about the origin.

Explanation:

Step1: Recall rotation rule

The rule for rotating a point $(x,y)$ 270° counter - clockwise about the origin is $(x,y)\to(y, - x)$.

Step2: Identify vertices of SORT

Let's assume the vertices of quadrilateral $SORT$ have coordinates. Suppose $S(x_1,y_1)$, $O(x_2,y_2)$, $R(x_3,y_3)$, $T(x_4,y_4)$.

Step3: Apply rotation rule to each vertex

For vertex $S(x_1,y_1)$, its image $S'(y_1,-x_1)$. For $O(x_2,y_2)$, its image $O'(y_2,-x_2)$. For $R(x_3,y_3)$, its image $R'(y_3,-x_3)$. For $T(x_4,y_4)$, its image $T'(y_4,-x_4)$.

Step4: Plot the new vertices

Plot the points $S'$, $O'$, $R'$, $T'$ on the same coordinate grid and connect them in order to form the rotated quadrilateral.

Since we don't have the exact coordinates of the vertices of $SORT$ given in numerical form, the general process to draw the rotated image is as above. To actually draw it, you would need to identify the coordinates of the vertices of the original quadrilateral $SORT$ from the graph and then apply the $(x,y)\to(y, - x)$ transformation to each vertex and plot the new points.

Answer:

Step1: Recall rotation rule

The rule for rotating a point $(x,y)$ 270° counter - clockwise about the origin is $(x,y)\to(y, - x)$.

Step2: Identify vertices of SORT

Let's assume the vertices of quadrilateral $SORT$ have coordinates. Suppose $S(x_1,y_1)$, $O(x_2,y_2)$, $R(x_3,y_3)$, $T(x_4,y_4)$.

Step3: Apply rotation rule to each vertex

For vertex $S(x_1,y_1)$, its image $S'(y_1,-x_1)$. For $O(x_2,y_2)$, its image $O'(y_2,-x_2)$. For $R(x_3,y_3)$, its image $R'(y_3,-x_3)$. For $T(x_4,y_4)$, its image $T'(y_4,-x_4)$.

Step4: Plot the new vertices

Plot the points $S'$, $O'$, $R'$, $T'$ on the same coordinate grid and connect them in order to form the rotated quadrilateral.

Since we don't have the exact coordinates of the vertices of $SORT$ given in numerical form, the general process to draw the rotated image is as above. To actually draw it, you would need to identify the coordinates of the vertices of the original quadrilateral $SORT$ from the graph and then apply the $(x,y)\to(y, - x)$ transformation to each vertex and plot the new points.