Vertices of ΔXYZ are X(1, -4), Y(-2, -1) and Z(3, 1). For each translation, give the vertices of ΔXYZ'....

Question

1. Vertices of ΔXYZ are X(1, -4), Y(-2, -1) and Z(3, 1). For each translation, give the vertices of ΔXYZ'. T(-4,-3)(ΔXYZ)
2. What translation rule maps A(9, -3) to A'(5, -1)?
3. What translation is shown below?
Give the coordinates of each image:
1. T(-3,-1)(ΔABC) for A(5, 0), B(-1, 2), C(6, -3)
2. T(-1,4)(ΔDEF) for D(3, 3), E(-2, 3), F(0, 2)

SnapAndSolve AI · Accepted Answer

1. Translated Vertices of ΔXYZ

Vertices of ΔXYZ are:

X(1, -4)
Y(-2, -1)
Z(3, 1)

Translation: T_(-4,-3)

X' = (1 - 4, -4 - 3) = (-3, -7)
Y' = (-2 - 4, -1 - 3) = (-6, -4)
Z' = (3 - 4, 1 - 3) = (-1, -2)

Vertices of ΔXYZ' are:

X'(-3, -7)
Y'(-6, -4)
Z'(-1, -2)

2. Translation Rule for A(9, -3) to A'(5, -1)

Let the translation be T_{(x, y)}.

To find the translation rule, we start with the coordinates:

A(9, -3) translates to A'(5, -1)

The translation vector can be determined as follows:

x-coordinate change: 5 - 9 = -4
y-coordinate change: -1 - (-3) = 2

Thus, the translation rule is:

T_{(-4, 2)}

3. Translations Given Below

1. Translation of ΔABC

Vertices of ΔABC are:

A(5, 0)
B(-1, 2)
C(6, -3)

Translation: T_(-3,-1)

A' = (5 - 3, 0 - 1) = (2, -1)
B' = (-1 - 3, 2 - 1) = (-4, 1)
C' = (6 - 3, -3 - 1) = (3, -4)

Vertices of ΔABC' are:

A'(2, -1)
B'(-4, 1)
C'(3, -4)

2. Translation of ΔDEF

Vertices of ΔDEF are:

D(3, 3)
E(-2, 3)
F(0, 2)

Translation: T_{(-1, 4)}

D' = (3 - 1, 3 + 4) = (2, 7)
E' = (-2 - 1, 3 + 4) = (-3, 7)
F' = (0 - 1, 2 + 4) = (-1, 6)

Vertices of ΔDEF' are:

D'(2, 7)
E'(-3, 7)
F'(-1, 6)

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Vertices of ΔXYZ are X(1, -4), Y(-2, -1) and Z(3, 1). For each translation, give the vertices of ΔXYZ'....

Answer

1. Translated Vertices of ΔXYZ

2. Translation Rule for A(9, -3) to A'(5, -1)

3. Translations Given Below

1. Translation of ΔABC

2. Translation of ΔDEF

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