Question

follow the guided instructions below to rotate the figure 180° counter - clockwise about the origin. now draw a line through the yellow center that is perpendicular to the line that you just drew.

Explanation:

Step1: Recall rotation rule

For a 180 - degree counter - clockwise rotation about the origin, the rule for a point $(x,y)$ is $(x,y)\to(-x,-y)$.

Step2: Rotate triangle vertices

Let the vertices of the triangle be $(x_1,y_1),(x_2,y_2),(x_3,y_3)$. After rotation, they become $(-x_1,-y_1),(-x_2,-y_2),(-x_3,-y_3)$. Plot these new points and connect them to form the rotated triangle.

Step3: Draw first line

Draw a line through the yellow center (origin in this case) and one of the vertices of the rotated triangle.

Step4: Draw perpendicular line

Use the property that if the slope of the first - drawn line is $m$, the slope of the perpendicular line is $-\frac{1}{m}$ (for non - vertical and non - horizontal lines). For a vertical first - drawn line, the perpendicular line is horizontal and vice - versa. Draw a line through the origin with the appropriate slope to be perpendicular to the first - drawn line.

This is a geometric construction task and requires manual drawing on the given coordinate plane following the above steps. Since it's a drawing task and not a numerical answer, the steps describe the process of completing the given instructions.

Answer:

Step1: Recall rotation rule

For a 180 - degree counter - clockwise rotation about the origin, the rule for a point $(x,y)$ is $(x,y)\to(-x,-y)$.

Step2: Rotate triangle vertices

Let the vertices of the triangle be $(x_1,y_1),(x_2,y_2),(x_3,y_3)$. After rotation, they become $(-x_1,-y_1),(-x_2,-y_2),(-x_3,-y_3)$. Plot these new points and connect them to form the rotated triangle.

Step3: Draw first line

Draw a line through the yellow center (origin in this case) and one of the vertices of the rotated triangle.

Step4: Draw perpendicular line

Use the property that if the slope of the first - drawn line is $m$, the slope of the perpendicular line is $-\frac{1}{m}$ (for non - vertical and non - horizontal lines). For a vertical first - drawn line, the perpendicular line is horizontal and vice - versa. Draw a line through the origin with the appropriate slope to be perpendicular to the first - drawn line.

This is a geometric construction task and requires manual drawing on the given coordinate plane following the above steps. Since it's a drawing task and not a numerical answer, the steps describe the process of completing the given instructions.