To translate a figure in the coordinate plane, we have to translate each of its vertices. Then, we have to connect the vertices to form the image.
Example 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.
Solution :
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'.
Example 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.
Solution :
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'.
Example 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.
Solution :
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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