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A design was constructed by using two rectangles ABDC and A'B'C'D'. Rectangle A'B'C'D' is the result of a translation of rectangle ABDC. The table of translations is shown below. Find the coordinates of points B and D'. Rectangle ABDC A (2.4) Rectangle A'B'D C A' (3.1) B (-5.1) B C(2-1) D(-6,-1) D Find Coordinate B

A design was constructed by using two rectangles ABDC and A'B'C'D'. Rectangle A'B-example-1
User Overactor
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The rectangle ABDC is translated to the rectangle A'B'D'C'

We are asked to find the missing coordinates of these rectangles.

A(2, 4) and A'(3, 1)

C(2, -1) and C'(3, -4)

If you notice the above coordinates you will see a pattern.

The x coordinate of the translated rectangle is 1 more than the original x coordinate. (2 + 1 = 3)

The y coordinate of the translated rectangle is 3 less than the original y coordinate. (4 - 3 = 1 and -1 - 3 = -4)

Similarly, we can find the coordinates of B by applying the reverse logic.

B'(-5, 1)

Subtract 1 from x coordinates and add 3 to the y coordinate.

B(-5 - 1, 1 + 3)

B(-6, 4)

We are given D(-6, -1) and we want to find the translated coordinates D'

Let us apply the pattern we found earlier.

D(-6, -1)

Add 1 to the x coordinate and subtract 3 to the y coordinate.

D'(-6 + 1, -1 - 3)

D'(-5, -4)

Therefore, the missing coordinates are

B(-6, 4)

D'(-5, -4)

Orignal to translated coordinates:

Add 1 to the x coordinate and subtract 3 to the y coordinate.

Translated to original coordinates:

Subtract 1 from x coordinates and add 3 to the y coordinate.

User Westwood
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