Question

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

Explanation:

Step1: Determine the translation rule for the pre - image

The translation rule for the image is \(T_{-4,3}(x,y)\), which means \(x'=x - 4\) and \(y'=y + 3\). To find the pre - image, we use the inverse rule \(x=x'+4\) and \(y=y'-3\).

Step2: Find the coordinates of the vertices of the pre - image

Assume the vertices of the image \(A'B'C'D'\):

• If we consider a general vertex \((x',y')\) of the image. For the pre - image vertex \((x,y)\), we have \(x=x'+4\) and \(y=y'-3\).
• Let's check each option:
• For the point \((-1,-2)\): If \(x=-1\) and \(y = - 2\), then for the image \(x'=-1 - 4=-5\) and \(y'=-2+3 = 1\).
• For the point \((7,1)\): If \(x = 7\) and \(y=1\), then \(x'=7 - 4 = 3\) and \(y'=1 + 3=4\).
• For the point \((-1,7)\): If \(x=-1\) and \(y = 7\), then \(x'=-1-4=-5\) and \(y'=7 + 3=10\) (not on the image).
• For the point \((-1,1)\): If \(x=-1\) and \(y = 1\), then \(x'=-1-4=-5\) and \(y'=1 + 3=4\) (not correct).
• For the point \((7,-2)\): If \(x = 7\) and \(y=-2\), then \(x'=7-4 = 3\) and \(y'=-2 + 3=1\).

Answer:

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