Question

1. the coordinates of the vertices of a quadrilateral are p(1,2), r(1,4), s(3,4), and t(4,2). quadrilateral prst is reflected across the y-axis to create quadrilateral prst. which rule describes this transformation? (x,y)→(x,−y) (x,y)→(−x,y) (x,y)→(y,−x) (x,y)→(−y,x)

Explanation:

Step1: Recall reflection over y - axis rule

The rule for reflecting a point \((x,y)\) across the \(y\) - axis is that the \(x\) - coordinate changes its sign while the \(y\) - coordinate remains the same. Mathematically, this is given by the transformation \((x,y)\to(-x,y)\).

Step2: Verify with a vertex

Let's take vertex \(P(1,2)\). After reflecting across the \(y\) - axis, the new \(x\) - coordinate should be \(- 1\) and the \(y\) - coordinate remains \(2\), so \(P'\) should be \((-1,2)\). Using the rule \((x,y)\to(-x,y)\), when \(x = 1\) and \(y=2\), we get \((-1,2)\), which matches. Let's check another vertex, say \(T(4,2)\). After reflection, \(T'\) should be \((-4,2)\). Using the rule \((x,y)\to(-x,y)\), when \(x = 4\) and \(y = 2\), we get \((-4,2)\), which is correct. The other rules: \((x,y)\to(x, - y)\) is reflection over \(x\) - axis, \((x,y)\to(y,-x)\) and \((x,y)\to(-y,x)\) are rotation rules, not reflection over \(y\) - axis.

Answer:

\((x,y)\to(-x,y)\) (the option with the filled circle: \((x,y)\to(-x,y)\))