Question

Perform the following transformations in the pictures below.

Answer 1

QUESTION A

ΔALT has coordinates $A(-5,-1),L(-3,-2),T(-3,2)$.

If we translate by the rule $(x,y)\rightarrow (x+6,y-3)$

Then;

$A(-5,-1)\rightarrow (-5+6,-1-3)=(1,-4)$.

$B(-3,-2)\rightarrow (-3+6,-2-3)=(3,-5)$.

$T(-3,2)\rightarrow (-3+6,2-3)=(3,-1)$.

A reflection over the y-axis has the mapping

$(x,y)\rightarrow (-x,y)$

If we reflect the resulting points over the y-axis, we obtain,

$A(-5,-1)\rightarrow (1,-4)\rightarrow A'(-1,-4)$.

$B(-3,-2)\rightarrow (3,-5)\rightarrow B'(-3,-5)$.

$T(-3,2)\rightarrow (3,-1)\rightarrow C'(-3,-1)$.

QUESTION B

ΔTAB has vertices $T(2,3),A(1,1),B(4,-3)$.

A reflection over the x-axis has the mapping

$(x,y)\rightarrow (x,-y)$

A reflection over the y-axis also has the mapping;

$(x,y)\rightarrow (-x,y)$

If we reflect ΔTAB over the x-axis and reflect the resulting image over the y-axis, we obtain;

$T(2,3)\rightarrow (2,-3) \rightarrow T'(-2,-3)$

$A(1,1)\rightarrow (1,-1) \rightarrow A'(-1,-1)$

$B(4,-3)\rightarrow (4,3) \rightarrow B'(-4,3)$

QUESTION C

ΔALT has vertices $A(-5,-1),L(-3,-2),T(-3,2)$.

A $90\degree$ clockwise rotation about the origin has the mapping;

$(x,y)\rightarrow (y,-x)$

A reflection in the line y=x also has the mapping;

$(x,y)\rightarrow (y,x)$

When we rotate the given triangle $90\degree$ clockwise about the origin, and then reflect the image over the line y=x, we obtain;

$A(-5,-1)\rightarrow (-1,5)\rightarrow A'(5,-1)$

$L(-3,-2)\rightarrow (-2,3)\rightarrow L'(3,-2)$

$T(-3,2)\rightarrow (2,3)\rightarrow T'(3,2)$

QUESTION D

ΔTAB has vertices $T(2,3),A(1,1),B(4,-3)$.

A reflection over the y-axis has the mapping;

$(x,y)\rightarrow (-x,y)$

The rule for the given translation is

$(x,y)\rightarrow (x+2,y-1)$

If reflect the given triangle over the y-axis and translate using the rule $(x,y)\rightarrow (x+2,y-1)$, we obtain;

$T(2,3)\rightarrow (-2,3)\rightarrow (-2+2,3-1)=T'(0,2)$

$A(1,1)\rightarrow (-1,1)\rightarrow (-1+2,1-1)=A'(1,0)$

$B(4,-3)\rightarrow (-4,-3)\rightarrow (-4+2,-3-1)=B'(-2,-4)$

Answer 2

I’m not sure, sorry!