Question

4 a circle is graphed on the coordinate plane with its center at (-4, 7). the circle will be translated p units to the right and v units down. which rule describes the center of the new circle after this translation?
a (x, y) → (-4 + p, 7 + v)
b (x, y) → (-4 + p, 7 − v)
c (x, y) → (-4 − p, 7 − v)
d (x, y) → (-4 − p, 7 + v)

5 a figure was transformed on a coordinate grid using the rule (x,y) -> (-x, -y) which description represents this transformation?
a a reflection across the x-axis
b a reflection across the y-axis
c a 90° clockwise rotation about the origin
d a 180° clockwise rotation about the origin

6 reflections preserve orientation.
a true
b false
c direction
d vertices

Explanation:

Question 4

Step1: Recall translation rules

In coordinate plane, translating a point \((x,y)\) \(p\) units right changes the \(x\)-coordinate by \(+p\) (since right is positive \(x\)-direction), and translating \(v\) units down changes the \(y\)-coordinate by \(-v\) (since down is negative \(y\)-direction).

Step2: Apply to center \((-4,7)\)

Original center is \((-4,7)\). After translating \(p\) units right, new \(x\)-coordinate is \(-4 + p\). After translating \(v\) units down, new \(y\)-coordinate is \(7 - v\). So the rule is \((x,y)\to(-4 + p,7 - v)\).

Step1: Recall transformation rules

• Reflection over \(x\)-axis: \((x,y)\to(x,-y)\)
• Reflection over \(y\)-axis: \((x,y)\to(-x,y)\)
• \(90^\circ\) clockwise rotation: \((x,y)\to(y,-x)\)
• \(180^\circ\) clockwise rotation: \((x,y)\to(-x,-y)\)

Step2: Match the given rule

The given rule is \((x,y)\to(-x,-y)\), which matches the \(180^\circ\) clockwise rotation about the origin.

Step1: Recall reflection and orientation

Reflections are a type of transformation that flip a figure over a line. Orientation refers to the order (clockwise or counterclockwise) of the vertices. Reflections reverse the orientation (e.g., a clockwise polygon becomes counterclockwise after reflection). So the statement "Reflections preserve orientation" is false.

Answer:

B. \((x, y) \to (-4 + p, 7 - v)\)

Question 5