Question

rotation: a rotation turns a point around a fixed point called the center of rotation. 1. rotate the triangle abc around point m 90 degrees clockwise. • hint: locate the center of rotation (m), mark it and draw a cross.

Explanation:

Step1: Identify center of rotation

Locate point \( m \) on the grid and mark it. This is the fixed point around which we rotate triangle \( ABC \).

Step2: Rotate point \( A \)

To rotate a point \((x,y)\) 90° clockwise around a center \((h,k)\), the formula is \((x', y')=(h + (y - k), k - (x - h))\). First, find the coordinates of \( A \) and \( m \). Let's assume \( m \) is at \((h,k)\) and \( A \) is at \((x_A,y_A)\). Calculate the vector from \( m \) to \( A \): \((x_A - h, y_A - k)\). After 90° clockwise rotation, this vector becomes \((y_A - k, -(x_A - h))\). So the new coordinates of \( A' \) (rotated \( A \)) are \((h + (y_A - k), k - (x_A - h))\). Plot this point.

Step3: Rotate point \( B \)

Repeat the same process for point \( B \). Let \( B \) have coordinates \((x_B,y_B)\). Vector from \( m \) to \( B \) is \((x_B - h, y_B - k)\). After 90° clockwise rotation, the vector is \((y_B - k, -(x_B - h))\). New coordinates of \( B' \) are \((h + (y_B - k), k - (x_B - h))\). Plot this point.

Step4: Rotate point \( C \)

For point \( C \) with coordinates \((x_C,y_C)\), vector from \( m \) to \( C \) is \((x_C - h, y_C - k)\). After 90° clockwise rotation, the vector is \((y_C - k, -(x_C - h))\). New coordinates of \( C' \) are \((h + (y_C - k), k - (x_C - h))\). Plot this point.

Step5: Connect the rotated points

Connect \( A' \), \( B' \), and \( C' \) to form the rotated triangle.

Answer:

The rotated triangle \( A'B'C' \) is drawn by rotating each vertex of \( ABC \) 90° clockwise around point \( m \) using the rotation formula for coordinates and then connecting the new vertices. (Note: Since this is a graphical task, the final answer is the drawn rotated triangle on the grid following the above steps.)