Question

rectangle abcd is the image of rectangle abcd after it has been translated according to the rule $t_{-4,3}(x,y)$. which points are vertices of the pre - image, rectangle abcd? select four options. $(-1,-2)$ $(7,1)$ $(-1,7)$ $(-1,1)$ $(7,-2)$

Explanation:

Step1: Understand the translation rule

The translation rule is \(T_{- 4,3}(x,y)=(x - 4,y + 3)\). To find the pre - image, we use the inverse rule \(T_{4,-3}(x',y')=(x'+4,y' - 3)\) where \((x',y')\) are the coordinates of the image.

Step2: Assume coordinates of image vertices

Let's assume the coordinates of \(A'(-5,4)\), \(B'(3,4)\), \(C'(3,1)\), \(D'(-5,1)\) (by looking at the graph).

Step3: Find pre - image coordinates

For \(A'\):
\(x=-5 + 4=-1\), \(y = 4-3 = 1\).
For \(B'\):
\(x=3 + 4=7\), \(y=4 - 3=1\).
For \(C'\):
\(x=3+4 = 7\), \(y=1 - 3=-2\).
For \(D'\):
\(x=-5 + 4=-1\), \(y=1 - 3=-2\).

Answer:

\((-1,-2)\), \((7,1)\), \((-1,1)\), \((7,-2)\)