Question

question one (1fd)
question two (2pts)
identify the transformation shown. give the written description for each.
question three (2pts)
a figure is translated on the coordinate plane. the rule for the
transformation is $(x,y)\to(x + 2,y - 5)$. if the pre - image is $a(2,3)$,
what are the coordinates of the image $a$?
answer
$a=$
question four (2pts)
a triangle $\triangle abc$ is reflected across the $y$ - axis. the vertex $b$ of the
pre - image is $(4, - 1)$. what are the coordinates of the image vertex,
$b$?
answer

Explanation:

Question Three

Step1: Apply the translation rule

The translation rule is \((x,y)\to(x + 2,y-5)\). For the point \(A(2,3)\), substitute \(x = 2\) and \(y=3\) into the rule.
For the \(x\)-coordinate of the image: \(x'=2 + 2\).
For the \(y\)-coordinate of the image: \(y'=3-5\).

Step2: Calculate the coordinates

\(x'=2+2 = 4\) and \(y'=3 - 5=-2\).

Question Four

Step1: Use the reflection rule across the \(y\)-axis

The rule for reflecting a point \((x,y)\) across the \(y\)-axis is \((x,y)\to(-x,y)\). Given the point \(B(4,-1)\), substitute \(x = 4\) and \(y=-1\) into the rule.
For the \(x\)-coordinate of the image: \(x'=-4\). The \(y\)-coordinate remains the same, so \(y'=-1\).

Answer:

• Question Three: \(A'=(4,-2)\)
• Question Four: \(B'=(-4,-1)\)