How to Rotate a Triangle 270° Clockwise About the Origin with Guided Steps

Question

Follow the guided instructions below to rotate the figure 270° clockwise about the origin. First step: Draw a circle centered at the center of rotation, such that one of the vertices of the figure is on the circle. The original triangle has vertices at (-6, 2), (-8, 3), (-2, 7).

Accepted Answer

1. Circle: Centered at (0,0) with radius equal to the distance from origin to one vertex (e.g., radius √((-2)^2 +7^2)=√53 for vertex (-2,7)); 2. Rotated triangle vertices: (2, 6), (3, 8), (7, 2); 3. Final rotated triangle plotted with these new vertices.

Answer

Step 1: Identify the original vertices of the triangle from the graph: Vertex A (-6, 2), Vertex B (-8, 3), Vertex C (-2, 7). Step 2: Draw the required circle: Choose one vertex, for example C (-2,7). Calculate its distance from the origin (0,0) using the distance formula d=√(x²+y²)=√((-2)²+7²)=√53. Draw a circle centered at (0,0) with radius √53, which will pass through point C. Step 3: Apply the 270° clockwise rotation rule about the origin: For any point (x,y), the rotated point (x',y') is given by (y, -x). Step 4: Calculate each rotated vertex: For A (-6,2): (2, 6); For B (-8,3): (3, 8); For C (-2,7): (7, 2). Step 5: Plot the new vertices (2,6), (3,8), (7,2) and connect them to form the rotated triangle.