Question

quiz 1 - cartesian coordinates, translation, and reflection
q1) what are the coordinates of corners of the house shape shown below:
a(1,1)
b(1,3)
c(5,3)
d(5,1)
e(4,6)
q2) the shape above is translated 3 steps to the right and 6 steps downward. what will be the new coordinates for:
a (, )
b (, )
c (, )
d (, )
e (, )

Explanation:

Step1: Understand the translation rule

When a point \((x,y)\) is translated \(a\) steps to the right and \(b\) steps downward, the new coordinates \((x',y')\) are given by the formula \(x'=x + a\) and \(y'=y - b\). Here \(a = 3\) and \(b=6\).

Step2: Calculate the new \(x\) - coordinate for each point

For point \(A(-7,1)\): \(x=-7+3=-4\)
For point \(B(-7,3)\): \(x=-7 + 3=-4\)
For point \(C(-3,3)\): \(x=-3+3=0\)
For point \(D(-3,1)\): \(x=-3+3=0\)
For point \(E(-5,6)\): \(x=-5+3=-2\)

Step3: Calculate the new \(y\) - coordinate for each point

For point \(A(-7,1)\): \(y=1-6=-5\)
For point \(B(-7,3)\): \(y=3 - 6=-3\)
For point \(C(-3,3)\): \(y=3-6=-3\)
For point \(D(-3,1)\): \(y=1-6=-5\)
For point \(E(-5,6)\): \(y=6-6=0\)

Answer:

\(A'(-4,-5)\)
\(B'(-4,-3)\)
\(C'(0,-3)\)
\(D'(0,-5)\)
\(E'(-2,0)\)