Rectangle ABCD has vertices in the standard (x,y) coordinate plane at A(−4,−2), B(−4,3), C(2,3), and D(2,−2). A translation of rectangle ABCD is a second rectangle, A′B′C′D′, with vertices A′(4,−12), B′(x,y), C′(10,−7), and D′(10,−12). What are the coordinates of B′ ?Responses(3,-6)(3,-6)(4,3)(4,3)(4,-7)(4,-7)(4,-13)(4,-13)(6,-5)
Question
Rectangle ABCD has vertices in the standard (x,y) coordinate plane at A(−4,−2), B(−4,3), C(2,3), and D(2,−2). A translation of rectangle ABCD is a second rectangle, A′B′C′D′, with vertices A′(4,−12), B′(x,y), C′(10,−7), and D′(10,−12). What are the coordinates of B′ ?Responses(3,-6)(3,-6)(4,3)(4,3)(4,-7)(4,-7)(4,-13)(4,-13)(6,-5)
Solution
The translation of a figure involves moving every point a constant distance in a specified direction. It does not change the figure's size or orientation.
To find the coordinates of B', we need to determine how far the rectangle was moved horizontally and vertically.
We can do this by comparing the coordinates of A and A'.
A is at (-4, -2) and A' is at (4, -12).
Horizontally, A was moved from -4 to 4, a shift of 8 units to the right.
Vertically, A was moved from -2 to -12, a shift of 10 units down.
So, to find the coordinates of B', we apply the same shifts to the coordinates of B.
B is at (-4, 3).
Moving 8 units to the right gives us a new x-coordinate of -4 + 8 = 4.
Moving 10 units down gives us a new y-coordinate of 3 - 10 = -7.
So, B' is at (4, -7).
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