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 - degree rotation

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

Step2: Analyze the \(x\) - coordinate of \(P\) and \(P'\)

The \(x\) - coordinate of \(P\) is \(x = 3\), and the \(x\) - coordinate of \(P'\) is \(x'=-3\). The \(y\) - coordinate of \(P\) is \(y = 1\), and the \(y\) - coordinate of \(P'\) is \(y'=-1\).
We can see that the \(x\) - coordinate of \(P'\) (\(-3\)) is the opposite of the \(x\) - coordinate of \(P\) (\(3\)), and the \(y\) - coordinate of \(P'\) (\(-1\)) is the opposite of the \(y\) - coordinate of \(P\) (\(1\)).

Answer:

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