Question

3
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?
a ((x,y)\to(x, - y))
b ((x,y)\to(-x,y))
c ((x,y)\to(y, - x))
d ((x,y)\to(-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 \(y\) - coordinate remains the same and the \(x\) - coordinate changes its sign. So the transformation rule is \((x,y)\to(-x,y)\).
We can also verify this with a point from the quadrilateral. Let's take point \(P(1,2)\). After reflecting across the \(y\) - axis, the new \(x\) - coordinate should be \(- 1\) and the \(y\) - coordinate remains \(2\), so \(P'(-1,2)\). Using the rule \((x,y)\to(-x,y)\) on \(P(1,2)\), we get \((-1,2)\), which matches.
For point \(R(1,4)\), reflecting across the \(y\) - axis gives \(R'(-1,4)\). Using the rule \((x,y)\to(-x,y)\) on \(R(1,4)\), we get \((-1,4)\), which is correct.
For point \(S(3,4)\), reflecting across the \(y\) - axis gives \(S'(-3,4)\). Using the rule \((x,y)\to(-x,y)\) on \(S(3,4)\), we get \((-3,4)\), which is correct.
For point \(T(4,2)\), reflecting across the \(y\) - axis gives \(T'(-4,2)\). Using the rule \((x,y)\to(-x,y)\) on \(T(4,2)\), we get \((-4,2)\), which is correct.

Step2: Analyze other options

• Option A: \((x,y)\to(x, - y)\) is the rule for reflection across the \(x\) - axis, not the \(y\) - axis.
• Option C: \((x,y)\to(y,-x)\) is a rotation (90 - degree counter - clockwise rotation), not a reflection across the \(y\) - axis.
• Option D: \((x,y)\to(-y,x)\) is also a rotation (90 - degree clockwise rotation), not a reflection across the \(y\) - axis.

Answer:

B. \((x,y)\to(-x,y)\)