Question

topic 3 review- do now
possible points: 3
match each transformation with its rule.
$r_{(x - axis)}(x,y)$
$r_{(y - axis)}(x,y)$
$r_{90^{circ}}(x,y)$
$r_{180^{circ}}(x,y)$
$r_{270^{circ}}(x,y)$
$t_{<2,3>}(x,y)$
::$(x + 2,y + 3)$ ::$(2x,2y)$ ::$(y,-x)$ ::$(-x,-y)$ ::$(-y,x)$ ::$(-x,y)$ ::$(x,-y)$

Explanation:

Step1: Reflection over x - axis

When reflecting a point \((x,y)\) over the \(x\) - axis, the \(x\) - coordinate remains the same and the \(y\) - coordinate changes its sign. So \(R_{(x - axis)}(x,y)=(x,-y)\)

Step2: Reflection over y - axis

When reflecting a point \((x,y)\) over the \(y\) - axis, the \(y\) - coordinate remains the same and the \(x\) - coordinate changes its sign. So \(R_{(y - axis)}(x,y)=(-x,y)\)

Step3: Rotation of \(90^{\circ}\) counter - clockwise

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

Step4: Rotation of \(180^{\circ}\)

The rule for a \(180^{\circ}\) rotation of a point \((x,y)\) about the origin is \((x,y)\to(-x,-y)\)

Step5: Rotation of \(270^{\circ}\) counter - clockwise

The rule for a \(270^{\circ}\) counter - clockwise rotation of a point \((x,y)\) about the origin is \((x,y)\to(y,-x)\)

Step6: Translation \(T_{\langle2,3

angle}\)
The rule for a translation \(T_{\langle a,b
angle}(x,y)=(x + a,y + b)\). For \(T_{\langle2,3
angle}(x,y)\), we have \(T_{\langle2,3
angle}(x,y)=(x + 2,y+3)\)

Answer:

\(R_{(x - axis)}(x,y)=(x,-y)\)

\(R_{(y - axis)}(x,y)=(-x,y)\)

\(r_{90^{\circ}}(x,y)=(-y,x)\)

\(r_{180^{\circ}}(x,y)=(-x,-y)\)

\(r_{270^{\circ}}(x,y)=(y,-x)\)

\(T_{\langle2,3
angle}(x,y)=(x + 2,y + 3)\)