Question

1. the point (a, b) is the top of a rectangle. after a transformation, it maps to the point (-a, b + 3), what type of transformations happened?

reflection over the line y = -1 and translated 3 units left
reflection over the y = 1 and translated 3 units right
reflection over the y - axis and translated 3 units up
reflection over the x - axis and translated 3 units down

Explanation:

• Reflection over the y - axis:
• The rule for reflection over the y - axis is \((x,y)\to(-x,y)\). For the point \((a,b)\), after reflection over the y - axis, it becomes \((-a,b)\).
• Translation:
• The rule for translation is \((x,y)\to(x,y + k)\) (vertical translation). Here, from \((-a,b)\) to \((-a,b + 3)\), we have \(k=3\), which means a translation of 3 units up.

Answer:

reflection over the y - axis and translated 3 units up