ALGEBRAIC REPRESENTATIONS OF TRANSLATIONS WORKSHEET

Problem 1 :

Triangle PQR has the vertices P(1, 11), Q(1, 7) and R(3, 7). Graph the triangle PQR and its image after a translation of 7 units to the right and 5 unit down.

Problem 2 :

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 3 :

Triangle ABC has the vertices A (-4, 1), B(0, -1) and C(-2, -3). Graph the triangle ABC and its image after a translation of 4 units to the right and 1 unit up.

1. Answer :

Step 1 :

Let P', Q' and R' be the vertices of the translated figure.

Since there is a translation of 7 units to the right and 5 units down, we have to add 7 to x-coordinate and subtract 5 from  y-coordinate of each vertex.

P' ------>  (1+7, 11-5)  =  (8, 6)

Q' ------>  (1+7, 7-5)  =  (8, 2)

R' ------>  (3+7, 7-5)  =  (10, 2)

Step 2 :

Sketch the triangle PQR and its image P'Q'R'.

2. 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'.

3. Answer :

Step 1 :

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

Since there is a translation of 4 units to the right and 1 unit up, we have to add 4 to x-coordinate and add 1 to y-coordinate of each vertex.

A' ------>  (-4+4, 1+1)  =  (0, 2)

B' ------>  (0+4, -1+1)  =  (4, 0)

C' ------>  (-2+4, -3+1)  =  (2, -2)

Step 2 :

Sketch the triangle ABC and its image A'B'C'.

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