Question

△pqr is rotated 180° around the origin to form △pqr. which coordinate is the same as the x-coordinate of point p? x-coordinate of point p; y-coordinate of point p; opposite of x-coordinate of point p; opposite of y-coordinate of point p

Explanation:

Step1: Recall 180° rotation rule

A 180° rotation around the origin transforms a point \((x, y)\) to \((-x, -y)\).

Step2: Analyze point P and P'

Point \(P\) has coordinates \((3, 1)\), and after 180° rotation, \(P'\) is \((-3, -1)\). The \(x\)-coordinate of \(P\) is \(3\), and we check the options:

• The \(x\)-coordinate of \(P\) is \(3\), \(P'\)'s \(x\)-coordinate is \(-3\), not the same.
• The \(y\)-coordinate of \(P\) is \(1\), not related to \(P'\)'s \(x\)-coordinate.
• The opposite of \(x\)-coordinate of \(P\) is \(-3\), which is the \(x\)-coordinate of \(P'\).
• The opposite of \(y\)-coordinate of \(P\) is \(-1\), which is \(P'\)'s \(y\)-coordinate, not \(x\)-coordinate.

Answer:

Opposite of \(x\)-coordinate of point \(P\) (the third option: "Opposite of \(x\)-coordinate of point \(P\)")