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 the rule for 180° rotation

When a point \((x,y)\) is rotated \(180^{\circ}\) around the origin, the new coordinates are \((-x,-y)\).
For point \(P(3,1)\), after \(180^{\circ}\) rotation, \(P'\) has coordinates \((-3,-1)\).

Step2: Compare coordinates

The \(x\) - coordinate of \(P\) is \(3\), and the \(x\) - coordinate of \(P'\) is \(- 3\) (opposite of \(x\) - coordinate of \(P\)). The \(y\) - coordinate of \(P\) is \(1\), and the \(y\) - coordinate of \(P'\) is \(-1\) (opposite of \(y\) - coordinate of \(P\)).

Answer:

Opposite of \(x\) - coordinate of point \(P\)