This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Let's find the image triangle A_2B_2C_2 by rotating triangle ABC 90^ anticlockwise about the origin. Step 1: Determine the rule for a 90^ anticlockwise rotation about the origin. An anticlockwise rotation of 90^ about the origin transforms a point (x,y) to (-y,x). Step 2: Apply the rotation rule to the vertices of triangle ABC. • For A(3,5): A_2 = (-5, 3) • For B(0,2): B_2 = (-2, 0) • For C(5,1): C_2 = (-1, 5) So, the vertices of the image triangle are A_2(-5,3), B_2(-2,0), and C_2(-1,5). Step 3: Plot the image points on your graph. • Plot A_2(-5,3): Move 5 units left from the origin, then 3 units up. Label it A_2(-5,3). • Plot B_2(-2,0): Move 2 units left from the origin, then stay on the x-axis. Label it B_2(-2,0). • Plot C_2(-1,5): Move 1 unit left from the origin, then 5 units up. Label it C_2(-1,5). Step 4: Draw triangle A_2B_2C_2. Connect the points A_2, B_2, and C_2 with straight lines to form the rotated triangle. Last free one today — make it count tomorrow, or type /upgrade for unlimited.