The locations of the vertices are shown below:
(- 5, 4), (- 4, 4), (- 5, 2)(- 4, 1), (- 1, 2), (0, - 1), (- 2, - 5)(2, 5), (3, 4), (1, 2)(3, - 5), (- 2, - 3), (0, - 1)What are the coordinates of the images resulting from a translation?
Herein we find four representations of polygons on Cartesian plane and we must determine the coordinates of the images generated by translation, a kind of rigid transformations. Translation is described by the following operation:
P'(x, y) = P(x, y) + T(x, y)
Where:
P(x, y) - Original pointP'(x, y) - Resulting pointT(x, y) - Translation vector
Case 1 (K(x, y) = (3, - 3), X(x, y) = (4, - 3), R(x, y) = (3, - 5), T(x, y) = (- 8, 7))
K'(x, y) = (3, - 3) + (- 8, 7) = (- 5, 4)
X'(x, y) = (4, - 3) + (- 8, 7) = (- 4, 4)
R'(x, y) = (3, - 5) + (- 8, 7) = (- 5, 2)
Case 2 (E(x, y) = (0, 2), X(x, y) = (3, 3), V(x, y) = (4, 0), Z(x, y) = (2, - 4), T(x, y) = (- 4, - 1))
E'(x, y) = (0, 2) + (- 4, - 1) = (- 4, 1)
X'(x, y) = (3, 3) + (- 4, - 1) = (- 1, 2)
V'(x, y) = (4, 0) + (- 4, - 1) = (0, - 1)
Z'(x, y) = (2, - 4) + (- 4, - 1) = (- 2, - 5)
Case 3 (G(x, y) = (- 4, 5), J(x, y) = (- 3, 4), U(x, y) = (- 5, 2), T(x, y) = (6, 0))
G'(x, y) = (- 4, 5) + (6, 0) = (2, 5)
J'(x, y) = (- 3, 4) + (6, 0) = (3, 4)
U'(x, y) = (- 5, 2) + (6, 0) = (1, 2)
Case 4 (V(x, y) = (0, 0), Y(x, y) = (- 5, 2), F(x, y) = (- 3, 4), T(x, y) = (3, - 5))
V'(x, y) = (0, 0) + (3, - 5) = (3, - 5)
Y'(x, y) = (- 5, 2) + (3, - 5) = (- 2, - 3)
F'(x, y) = (- 3, 4) + (3, - 5) = (0, - 1)
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Answer:
See attachments.
Step-by-step explanation:
A translation is a type of transformation that moves a figure left, right, up or down. Every point on the original figure is translated (moved) by the same distance in the same direction.
If a figure is to be moved left, subtract the number of units it is to be moved from the x-values.If a figure is to be moved right, add the number of units it is to be moved to the x-values.If a figure is to be moved up, add the number of units it is to be moved to the y-values.If a figure is to be moved down, subtract the number of units it is to be moved from the y-values.
Question 1
Coordinates of the given pre-image:
K = (3, -3)R = (3, -5)X = (4, -3)
Given mapping rule:
[tex](x, y) \rightarrow (x-8, y+7)[/tex]
This tells us to subtract 8 from the x-values and add 7 to the y-values.
[tex]\sf \implies K(3,-3) \rightarrow K'(3-8, -3+7)=K'(-5,4)[/tex]
[tex]\sf \implies R(3,-5) \rightarrow R'(3-8, -5+7)=R'(-5,2)[/tex]
[tex]\sf \implies X(4,-3) \rightarrow X'(4-8, -3+7)=X'(-4,4)[/tex]
Question 2
Coordinates of the given pre-image:
E = (0, 1)X = (3, 3)V = (4, 0)Z = (2, -4)
Given mapping rule:
[tex](x, y) \rightarrow (x-4, y-1)[/tex]
This tells us to subtract 4 from the x-values and subtract 1 from the y-values.
[tex]\sf \implies E(0,1) \rightarrow E'(0-4, 1-1)=E'(-4,0)[/tex]
[tex]\sf \implies X(3,3) \rightarrow X'(3-4, 3-1)=X'(-1,2)[/tex]
[tex]\sf \implies V(4,0) \rightarrow V'(4-4, 0-1)=V'(0,-1)[/tex]
[tex]\sf \implies Z(2,-4) \rightarrow Z'(2-4, -4-1)=Z'(-2,-5)[/tex]
Question 3
Coordinates of the given pre-image:
G = (-4, 5)J = (-3, 4)U = (-5, 2)
Given mapping rule:
[tex](x, y) \rightarrow (x+6, y)[/tex]
This tells us to add 6 to the x-values and the y-values remain unchanged.
[tex]\sf \implies G(-4,5) \rightarrow G'(-4+6, 5)=G'(2,5)[/tex]
[tex]\sf \implies J(-3,4) \rightarrow J'(-3+6, 4)=J'(3,4)[/tex]
[tex]\sf \implies U(-5,2) \rightarrow U'(-5+6, 2)=U'(1,2)[/tex]
Question 4
Coordinates of the given pre-image:
F = (-3, 4)V = (0, 0)Y = (-5, 2)
Given mapping rule:
[tex](x, y) \rightarrow (x+3, y-5)[/tex]
This tells us to add 3 to the x-values and subtract 5 from the y-values.
[tex]\sf \implies F(-3,4) \rightarrow F'( -3+3, 4-5)=F'(0,-1)[/tex]
[tex]\sf \implies V(0,0) \rightarrow V'( 0+3, 0-5)=V'(3,-5)[/tex]
[tex]\sf \implies Y(-5,2) \rightarrow Y'( -5+3, 2-5)=Y'(-2,-3)[/tex]
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