Question

1. a figure on a coordinate plane was transformed using the rule $(x,y)\to(-x,y)$. which best

describes the transformation?
a. a rotation $90^{circ}$ clockwise
b. a reflection over the x - axis
c. a rotation $180^{circ}$ clockwise
d. a reflection over the y - axis

1. which correctly describes the sequence of transformations

used to create the image on the graph?
a. reflection over the y - axis and a rotation $90^{circ}$ counterclockwise
b. translation 10 units right and a reflection over the x - axis
c. rotation $90^{circ}$ clockwise and a reflection over the x - axis
d. reflection over the x - axis and a translation 6 units right

Explanation:

Question 19

• For a reflection over the \(y\)-axis, the rule is \((x,y)\to(-x,y)\).
• A rotation \(90^{\circ}\) clockwise has the rule \((x,y)\to(y, -x)\).
• A reflection over the \(x\)-axis has the rule \((x,y)\to(x,-y)\).
• A rotation \(180^{\circ}\) clockwise has the rule \((x,y)\to(-x,-y)\).

• Let's assume a general point \((x,y)\) in rectangle \(WXYZ\).
• First, reflection over the \(x\)-axis: \((x,y)\to(x, -y)\).
• Then, translation \(6\) units right: \((x,-y)\to(x + 6,-y)\).
• For option A: Reflection over \(y\)-axis \((x,y)\to(-x,y)\) and rotation \(90^{\circ}\) counter - clockwise \((-x,y)\to(-y,-x)\) does not match.
• For option B: Translation \(10\) units right \((x,y)\to(x + 10,y)\) and reflection over \(x\)-axis \((x + 10,y)\to(x + 10,-y)\) does not match.
• For option C: Rotation \(90^{\circ}\) clockwise \((x,y)\to(y,-x)\) and reflection over \(x\)-axis \((y,-x)\to(y,x)\) does not match.

Answer:

D. A reflection over the \(y\)-axis

Question 20