Question

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)

Answer 1

Option B. (-1, 0)

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.

Answer 2

Option B

Explanation:

ABCD is a parallelogram with vertices as given

A =(0,1)

I transformation: Translated 1 unit to right. By this A (0,1) becomes

A(0+1,1) = (1,1)

II transformation: 1 unit down.

By this revised A (1,1) becomes (1,1-1) = (1,0)

III transformation: Rotated 180 degrees clockwise around the origin

Now new position of A, A" would be (-1,0)

Hence option B is right