Question

△pin is rotated −270° about the origin. draw the image of this rotation.

Explanation:

Step1: Recall rotation rule

A rotation of $- 270^{\circ}$ about the origin is equivalent to a rotation of $90^{\circ}$ clock - wise. The rule for a $90^{\circ}$ clock - wise rotation of a point $(x,y)$ about the origin is $(x,y)\to(y, - x)$.

Step2: Find the new coordinates of point P

Let's assume the coordinates of point $P$ are $(2,3)$. Using the rotation rule $(x,y)\to(y, - x)$, the new coordinates of $P$ are $(3,-2)$.

Step3: Find the new coordinates of other points

Suppose the other two vertices of $\triangle PIN$ have coordinates $(x_1,y_1)$ and $(x_2,y_2)$. Apply the rule $(x,y)\to(y, - x)$ to each of them to get their new coordinates $(y_1,-x_1)$ and $(y_2,-x_2)$.

Step4: Plot the new points

Plot the new points obtained from the above steps on the same coordinate grid and connect them to form the rotated triangle.

Since this is a drawing task and we can't actually draw in this text - based format, the steps above describe how to find the new points for the rotated triangle. To actually answer the question, one would follow these steps to plot the points on the given grid.

Answer:

Step1: Recall rotation rule

A rotation of $- 270^{\circ}$ about the origin is equivalent to a rotation of $90^{\circ}$ clock - wise. The rule for a $90^{\circ}$ clock - wise rotation of a point $(x,y)$ about the origin is $(x,y)\to(y, - x)$.

Step2: Find the new coordinates of point P

Let's assume the coordinates of point $P$ are $(2,3)$. Using the rotation rule $(x,y)\to(y, - x)$, the new coordinates of $P$ are $(3,-2)$.

Step3: Find the new coordinates of other points

Suppose the other two vertices of $\triangle PIN$ have coordinates $(x_1,y_1)$ and $(x_2,y_2)$. Apply the rule $(x,y)\to(y, - x)$ to each of them to get their new coordinates $(y_1,-x_1)$ and $(y_2,-x_2)$.

Step4: Plot the new points

Plot the new points obtained from the above steps on the same coordinate grid and connect them to form the rotated triangle.

Since this is a drawing task and we can't actually draw in this text - based format, the steps above describe how to find the new points for the rotated triangle. To actually answer the question, one would follow these steps to plot the points on the given grid.