Question

(a)
part a
what is the coordinate rule for this? (over the y-axis:)
a ((x, y) \to (x, -y))
b ((x, y) \to (-x, y))
c ((x, y) \to (-x, -y))
d ((x, y) \to (y, x))

(b)
part b
the point ((2, 0)) would map to what point?
a ((0, 2))
b ((0, -2))
c ((-2, 0))

8
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 x-axis. which rule represents this reflection?
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:

Part A

Step1: Recall reflection over y - axis rule

When a point \((x,y)\) is reflected over the \(y\) - axis, the \(x\) - coordinate changes its sign and the \(y\) - coordinate remains the same. So the rule is \((x,y)\to(-x,y)\).

Step2: Analyze options

• Option A: \((x,y)\to(x, - y)\) is reflection over \(x\) - axis.
• Option B: \((x,y)\to(-x,y)\) matches the reflection over \(y\) - axis rule.
• Option C: \((x,y)\to(-x,-y)\) is reflection over the origin.
• Option D: \((x,y)\to(y,x)\) is reflection over the line \(y = x\).

Step1: Use the reflection over y - axis rule

From Part A, the rule for reflection over \(y\) - axis is \((x,y)\to(-x,y)\).

Step2: Substitute \(x = 2\) and \(y=0\)

Substitute \(x = 2\) and \(y = 0\) into the rule \((x,y)\to(-x,y)\). We get \((-2,0)\).

Step1: Recall reflection over x - axis rule

When a point \((x,y)\) is reflected over the \(x\) - axis, the \(y\) - coordinate changes its sign and the \(x\) - coordinate remains the same. The rule is \((x,y)\to(x,-y)\).

Step2: Analyze options

• Option A: \((x,y)\to(x, - y)\) matches the reflection over \(x\) - axis rule.
• Option B: \((x,y)\to(-x,y)\) is reflection over \(y\) - axis.
• Option C: \((x,y)\to(y,-x)\) is not a standard reflection rule.
• Option D: \((x,y)\to(-y,x)\) is not a standard reflection rule.

Answer:

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

Part B