rectangle abcd is the image of rectangle abcd after it has been translated according to the rule…

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)

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)

Answer

Explanation:

Step1: Understand the translation rule

The rule $T_{- 4,3}(x,y)=(x - 4,y + 3)$. To find the pre - image, we need to reverse the rule. The reverse rule is $(x,y)\to(x + 4,y-3)$.

Step2: Check each option

Let's check each point:

  • For point $(-1,-2)$: Applying the reverse - rule, $x=-1,y = - 2$, then $(-1 + 4,-2-3)=(3,-5)$.
  • For point $(7,1)$: Applying the reverse - rule, $x = 7,y=1$, then $(7 + 4,1 - 3)=(11,-2)$.
  • For point $(-1,7)$: Applying the reverse - rule, $x=-1,y = 7$, then $(-1+4,7 - 3)=(3,4)$.
  • For point $(-1,1)$: Applying the reverse - rule, $x=-1,y = 1$, then $(-1 + 4,1-3)=(3,-2)$.
  • For point $(7,-2)$: Applying the reverse - rule, $x = 7,y=-2$, then $(7 + 4,-2-3)=(11,-5)$.

We can also find the vertices of the image rectangle $A'B'C'D'$ first. Assume $A'(-5,4),B'(3,4),C'(3,1),D'(-5,1)$. Applying the reverse - rule $T_{4,-3}(x,y)=(x + 4,y-3)$:

  • For $A'(-5,4)$: $(-5 + 4,4-3)=(-1,1)$
  • For $B'(3,4)$: $(3 + 4,4-3)=(7,1)$
  • For $C'(3,1)$: $(3 + 4,1-3)=(7,-2)$
  • For $D'(-5,1)$: $(-5 + 4,1-3)=(-1,-2)$

Answer:

A. $(-1,-2)$ B. $(7,1)$ D. $(-1,1)$ E. $(7,-2)$