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)

Explanation:

Step1: Identify the original coordinates

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

Step2: Apply the rotation formula

For a \( 180^{\circ} \) rotation \((x,y)\to(-x,-y)\). Substitute \( x=-5 \) and \( y = 7 \) into the formula.
When \( x=-5 \), \(-x=-(-5)=5\); when \( y = 7 \), \(-y=-7\).

Answer:

\((5,-7)\)