Question

a trapezoid in quadrant iii rotates 180° clockwise about the origin. what effect does the rotation have on the signs of the coordinate
a the signs change from negative to positive.
b the signs change from positive to negative.
c only the x - coordinates sign changes from negative to positive.
d only the y - coordinates sign changes from negative to positive.

Explanation:

Step1: Recall the rule for 180° rotation

When a point \((x,y)\) is rotated \(180^{\circ}\) clockwise about the origin, the new point is \((-x,-y)\).

Step2: Analyze the coordinates in Quadrant III

In Quadrant III, the coordinates of a point are \((x,y)\) where \(x<0\) and \(y < 0\). After a \(180^{\circ}\) rotation, the new coordinates are \((-x,-y)\). Since \(x<0\), \(-x>0\) and since \(y < 0\), \(-y>0\).

Answer:

A. The signs change from negative to positive.