Question

unit 1: rigid transformations and... a figure is transformed on the coordinate plane. match the transformation to the rule. a reflection across the y-axis a translation 4 units to the right and 7 units down a translation 3 units up a 90° counterclockwise rotation about the origin :: (x,y) → (x + 3, y) :: (x,y) → (-x, y) :: (x,y) → (x − 7, y + 4) :: (x,y) → (-y, x) :: (x,y) → (x, −y) :: (x,y) → (-x, −y) :: (x,y) → (x + 4, y − 7) :: (x,y) -

Explanation:

Step1: Analyze reflection across y - axis

A reflection across the \(y\) - axis changes the \(x\) - coordinate's sign while keeping the \(y\) - coordinate the same. So the rule for a reflection across the \(y\) - axis is \((x,y)\to(-x,y)\).

Step2: Analyze translation 4 units right and 7 units down

For a translation, moving \(h\) units right means adding \(h\) to the \(x\) - coordinate and moving \(k\) units down means subtracting \(k\) from the \(y\) - coordinate. Here, \(h = 4\) and \(k=7\), so the rule is \((x,y)\to(x + 4,y-7)\).

Step3: Analyze translation 3 units up

Moving \(k\) units up means adding \(k\) to the \(y\) - coordinate. Here \(k = 3\) and the \(x\) - coordinate remains the same. So the rule is \((x,y)\to(x + 3,y)\).

Step4: Analyze \(90^{\circ}\) counter - clockwise rotation about the origin

The rule for a \(90^{\circ}\) counter - clockwise rotation about the origin is \((x,y)\to(-y,x)\).

Answer:

• a reflection across the \(y\) - axis: \((x,y)\to(-x,y)\)
• a translation 4 units to the right and 7 units down: \((x,y)\to(x + 4,y - 7)\)
• a translation 3 units up: \((x,y)\to(x+3,y)\)
• a \(90^{\circ}\) counterclockwise rotation about the origin: \((x,y)\to(-y,x)\)