Question

13 reflections preserve congruence.
a true
b false
c sometimes
14 which rule represents a reflection over the y-axis?
a ((x, y))
b ((x, -y))
c ((-x, y))
d ((-x, -y))
15 which rule represents a reflection over the x-axis?
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:

Question 13

Reflections are a type of rigid transformation. Rigid transformations (like reflections, translations, rotations) preserve the shape and size of a figure, meaning they preserve congruence. So the statement "Reflections preserve congruence" is true.

When reflecting a point \((x,y)\) over the \(y\)-axis, the \(y\)-coordinate remains the same, and the \(x\)-coordinate is negated. So the rule is \((x,y)\to(-x,y)\).

• Option A is the original point, not a reflection.
• Option B is reflection over the \(x\)-axis.
• Option D is reflection over the origin.

When reflecting a point \((x,y)\) over the \(x\)-axis, the \(x\)-coordinate remains the same, and the \(y\)-coordinate is negated. So the rule is \((x,y)\to(x, -y)\).

• Option B is reflection over the \(y\)-axis.
• Option C and D are not standard reflection rules over the \(x\) or \(y\)-axis (they are related to rotations or other transformations).

Answer:

A. True

Question 14