Question

your turn

1. use coordinate notation to write the rule that maps each preimage to its image. then identify the transformation. graph the image rst to check your answer.

the coordinate rule is: (x,y) -> (x,y)
the transformation is:
preimage image
r(-4,3) -> r(1,-1)
s(-1,3) -> s(4,-1)
t(-4,1) -> t(1,-3)
for the x - value by how much do we add by to make - 4 to 1?
for the y - value by how much do we subtract by to make 3 to - 1?

1. draw the image of each figure under the given transformation. record the coordinate of the image pqr on the table.

(x,y) -> (x + 1,y + 2)
up or down?
left? right?
preimage image
p(-4,2) -> p()
q(-1,3) -> q()
r(-3,-3) -> r()

Explanation:

Step1: Find x - transformation for first problem

To get from \(x=-4\) (in \(R(-4,3)\)) to \(x = 1\) (in \(R'(1,-1)\)), we calculate \(1-(-4)=5\). So the \(x\) - coordinate transformation is \(x\to x + 5\).

Step2: Find y - transformation for first problem

To get from \(y = 3\) (in \(R(-4,3)\)) to \(y=-1\) (in \(R'(1,-1)\)), we calculate \(3-(-1)=4\). So the \(y\) - coordinate transformation is \(y\to y-4\). The coordinate rule is \((x,y)\to(x + 5,y - 4)\). This is a translation.

Step3: Apply transformation rule for second problem to point \(P\)

Given the transformation \((x,y)\to(x + 1,y + 2)\) and \(P(-4,2)\), for the \(x\) - coordinate of \(P'\), we have \(x=-4+1=-3\), and for the \(y\) - coordinate of \(P'\), we have \(y=2 + 2=4\). So \(P'(-3,4)\).

Step4: Apply transformation rule for second problem to point \(Q\)

Given \(Q(-1,3)\), for the \(x\) - coordinate of \(Q'\), we have \(x=-1+1 = 0\), and for the \(y\) - coordinate of \(Q'\), we have \(y=3 + 2=5\). So \(Q'(0,5)\).

Step5: Apply transformation rule for second problem to point \(R\)

Given \(R(-3,-3)\), for the \(x\) - coordinate of \(R'\), we have \(x=-3+1=-2\), and for the \(y\) - coordinate of \(R'\), we have \(y=-3 + 2=-1\). So \(R'(-2,-1)\).

Answer:

1. The coordinate rule is: \((x,y)\to(x + 5,y - 4)\)

The transformation is: Translation

1. \(P'(-3,4)\)

\(Q'(0,5)\)
\(R'(-2,-1)\)