A vector given in component form is presented as <x, y>, where x represent the horizontal displacement and y represents the vertical displacement
The vector that maps the figure ABCD to its image A'B'C'D' is <3, -7>
The reason the above value is correct is as follows:
The coordinates of the vertices of the preimage ABCD are A(-6, 4), B(-1, 4), C(3, 1), and D(-5, 1)
The coordinates of the vertices of the image A'B'C'D' are A'(-3, -3), B'(2, -3), C'(6, -6), and D'(-2, -6)
The component form of the vector that maps the figure to its image is given as follows;
[tex]\begin{array}{|c|r|l|c|}Differences&x-value \, (I_x - P_x)& y - value \, (I_y - P_y)& Vector\\A' \ and \ A &-3 - (-6) = 3&-3 - 4 = -7& <3, -7>\\B' \ and \ B&2 - (-1) = 3&-3 - 4 = -7&<3, -7>\\C' \ and \ C&6 - 3 = 3&-6 - 1 = -7&<3, -7>\\D' \ and \ D&-2 - (-5) = 3&-6 - 1 = -7&<3, -7>\end{array}[/tex]
Therefore,
The component form of the vector that maps the figure ABCD to its image A'B'C'D' is <3, -7>
Learn more about the component form of a vector here:
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