Parallelogram abcd has vertex coordinates a(0, 1), b(1, 3), c(4, 3), and d(3, 1). it is translated 1 unit to the right and 1 unit down and then roared 180 degrees clockwise around the origin. what are the coordinates of a "?

a. (0, -1)
b. (-1, 0)
c. (0, 1)
d. (1, 0)

Option B. (-1, 0)

Step-by-step explanation:

A parallelogram having vertices as A, B, C, D. We have to find the coordinates of A after transformations given in the question.

We will concentrate on the coordinates of A(0, 1) only.

1). A was translated 1 unit to the right.

It means new coordinates of vertex A become [(0 + 1), 1]. Here only x coordinates of vertex A gets changed. Y remains the same.

2). New vertex of A is transformed 1 unit down.

Now y coordinates of new vertex will become [1, (1 - 1)] = (1, 0)

3). Finally A is rotated by 180° clockwise around the origin.

Since point A lies in 1st quadrant so after 180° rotation point will lie in second quadrant. x coordinate will become negative by sign.

Finally vertex A will become as (-1, 0).

Option B. (-1, 0) is the correct option.

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