Question

the coordinates of a quadrilateral are (5,8), (7,10), (9,12), and (11,14). after a transformation, the sign of the x - coordinate and the sign of the y - coordinate for each ordered pair have changed. which type of transformation occurred?
a 180° rotation
b (x,y)→(x + 2,y + 2)
c reflection across the y - axis
d reflection across the x - axis

Explanation:

Step1: Analyze each transformation

• Option A (180° rotation): The rule for a 180° rotation about the origin is \((x,y)\to(-x,-y)\). This changes the sign of both \(x\) and \(y\) coordinates.
• Option B \((x,y)\to(x + 2,y+2)\): This is a translation (shift) of 2 units in the \(x\) - direction and 2 units in the \(y\) - direction. It does not change the sign of the coordinates.
• Option C (reflection across the \(y\) - axis): The rule is \((x,y)\to(-x,y)\). Only the \(x\) - coordinate sign changes.
• Option D (reflection across the \(x\) - axis): The rule is \((x,y)\to(x,-y)\). Only the \(y\) - coordinate sign changes.

Answer:

A. 180° rotation