ALGEBRAIC REPRESENTATIONS OF TRANSFORMATIONS WORKSHEET

Problem 1 :

Trapezoid ABCD has the vertices A (1, 0), B(4, 0), C(4, -4) and D(0, -4). Graph the trapezoid ABCD and its image after a translation of 5 units to the left and 3 units up.

Problem 2 :

A pentagon has the vertices A(-5, 6), B(-3, 6), C(-2, 4), D(-3, 1) and E(-5,1). Find the vertices of rectangle A'B'C'D'E' after a reflection across the y-axis. Then graph the pentagon and its image.

Problem 3 :

The triangle XYZ has the following vertices X(0, 0), Y(2, 0) and Z(2, 4). Rotate the triangle XYZ 90° counterclockwise about the origin.

Problem 4 :

A quadrilateral has the following vertices A(0, 0), B(1, 2), C(4, 2) and D(3, 0). Rotate the quadrilateral 180° clockwise about the origin.

1. Answer :

Step 1 :

Let A', B', C' and D' be the vertices of the translated figure.

Since there is a translation of 5 units to the left and 3 units up, we have to subtract 5 from x-coordinate and add 3 to y-coordinate of each vertex.

A' ------>  (1-5, 0+3)  =  (-4, 3)

B' ------>  (4-5, 0+3)  =  (-1, 3)

C' ------>  (4-5, -4+3)  =  (-1, -1)

D' ------>  (0-5, -4+3)  =  (-5, -1)

Step 2 :

Sketch the trapezoid ABCD and its image A'B'C'D'.

2. Answer :

Step 1 :

Apply the rule to find the vertices of the image.

Since there is a reflection across the y-axis, we have to multiply each x-coordinate by -1.

That is, (x, y) ----> (-x, y).

Step 2 :

A(-5, 6) ----> A'(5, 6)

B(-3, 6) ----> B'(3, 6)

C(-2, 4) ----> C'(2, 4)

D(-3, 1) ----> D'(3, 1)

E(-5, 1) ----> E'(5, 1)

Step 3 :

Graph the pentagon ABCDE and its image.

3. Answer :

Step 1 :

Trace triangle XYZ and the x- and y-axes onto a piece of paper.

Step 2 :

Let X', Y' and Z' be the vertices of the rotated figure.

Since the triangle is rotated 90° counterclockwise about the origin, the rule is

(x, y) ------> (-y, x)

Step 3 :

X(0, 0) ------> X'(0, 0)

Y(2, 0) ------> Y'(0, 2)

Z(2, 4) ------> Z'(-4, 2)

Step 4 :

Sketch the image X'Y'Z' using the points X'(0, 0),  Y'(0, 2) and  Z'(-4, 2).

4. Answer :

Step 1 :

Trace the quadrilateral ABCD and the x- and y-axes onto a piece of paper.

Step 2 :

Let A', B', C' and D' be the vertices of the rotated figure.

Since the quadrilateral is rotated 180° clockwise about the origin, the rule is

(x, y) ------> (-x, -y)

Step 3 :

A(0, 0) ------> A'(0, 0)

B(1, 2) ------> B'(-1, -2)

C(4, 2) ------> C'(-4, -2)

D(3, 0) ------> D'(-3, 0)

Step 4 :

Sketch the image A'B'C'D' using the points A'(0, 0), B'(-1, -2), C(-4, -2) and  D'(-3, 0).

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