Question

△ghi will be rotated 180° around the origin to form △ghi. 180° rotation: (x,y)→(-x,-y) what are the coordinates of point h after the rotation? (7,-5) (5,-7) (-7,-5) (5,7) h (-5,7) g i y 0 x

Explanation:

Step1: Identify the original coordinates

The original coordinates of point \( H \) are \( (-5, 7) \).

Step2: Apply the \( 180^\circ \) rotation rule

The rule for a \( 180^\circ \) rotation around the origin is \( (x, y) \to (-x, -y) \). For \( x = -5 \) and \( y = 7 \), we calculate \( -x = -(-5)=5 \) and \( -y = -7 \).

Answer:

\( (5, -7) \)