Translation questions are provided here, along with detailed explanations and suitable images for easy understanding. As we know, translation is one of the most commonly used concepts in the transformation of images on the coordinate system. Let’s practise some interesting translation questions.
What is meant by Translation in maths?
Translation refers to the displacement of the given figure on a coordinate plane from one place to another, without changing the orientation of the original figure. This means that the shape of the figure will not change by the translation.
Also, read: Translation
Translation Questions and Answers
1. Translate the rectangle A by 4 squares left and 3 squares up.
Solution:
The given rectangle A should be translated by 4 squares left and 3 squares up. That means translation by (-4, 3).
The given rectangle has the following vertices:
(2, 1), (3, 1), (3, -1) and (2, -1)
T = (-4, 3)
New vertices will be:
(2, 1) = (2 – 4, 1 + 3) = (-2, 4)
(3, 1) = (3 – 4, 1 + 3) = (-1, 4)
(3, -1) = (3 – 4, -1 + 3) = (-1, 2)
(2, -1) = (2 – 4, -1 + 3) = (-2, 2)
Thus, the required translated rectangle A’ is as follows.
2. Find the translation of polygon A by 4 squares up.
Solution:
The polygon in the given figure has the vertices (-3, -2), (-2, -2), (-1, -3) and (-4, -3).
Now, we have to move the polygon by 4 squares up.
So, the new vertices will be:
(-3, -2) = (-3, -2 + 4) = (-3, 2)
(-2, -2) = (-2, -2 + 4) = (-2, 2)
(-1, -3) = (-1, -3 + 4) = (-1, 1)
(-4, -3) = (-4, -3 + 4) = (-4, 1)
Hence, the translated polygon A’ is given below:
3. A(-2, 1), B(2, 4) and C(4, 2) are the three vertices of a triangle. If this triangle is translated by 2 squares right and 3 squares up, i.e., T(2, 3), what will be the new vertices of the triangle?
Solution:
Given vertices of the triangle are:
A(-2, 1), B(2, 4) and C(4, 2)
Now, the triangle is translated by 2 squares right and 3 squares up, i.e., T(2, 3).
So, the new vertices of the triangle are:
A(-2, 1) = (-2 + 2, 1 + 3) = (0, 4)
B(2, 4) = (2 + 2, 4 + 3) = (4, 7)
C(4, 2) = (4 + 2, 2 + 3) = (6, 5)
Therefore, the new vertices of the translated triangle are A'(0, 4), B'(4, 7) and C'(6, 5).
4. What is the rule of translation from the triangle RST to the other triangle R’S’T’?
Solution:
In the given figure, the coordinates of the vertices of triangle RST are:
R = (-3, 3)
S = (1, 2)
T = (-2, 1)
Vertices of the triangle R’S’T’ are:
R’ = (1, 1)
S’ = (5, 0)
T’ = (2, -1)
From the above, we can say that the x-coordinate of the vertices increased by 4 and the y-coordinates decreased by 2. That means, the triangle RST is translated by 4 squares right and 2 squares down, i.e., T(4, -2).
5. Point P(-6, 3) is translated by 6 units left and 4 units up. What are the coordinates of the translated point?
Solution:
Given point: P(-6, 3)
The given point is translated by 6 units left and 4 units up.
That means, we have to subtract 6 from the x-coordinate and add 4 to the y-coordinate.
Thus, the coordinates of the point P after the translation are:
P(-6, 3) = (-6 – 4, 3 + 4) = (-10, 7)
6. The coordinates of the line segment joining the points are P(-7, 4) and Q(-1, 8). If the line segment is translated by 5 units right and 3 units down, find the new coordinates.
Solution:
Given coordinates of the line segment joining the points are:
P(-7, 4) and Q(-1, 8)
Also, given that the line segment is translated by 5 units right and 3 units down.
That means, we need to add 5 to the x-coordinates and subtract 3 from the y-coordinates.
Thus, new coordinates will be:
P(-7, 4) = (-7 + 5, 4 – 3) = (-2, 1)
Q(-1, 8) = (-1 + 5, 8 – 3) = (4, 5)
7. What are the coordinates of the new line segment formed by the translation of the given line segment by 4 units left and 5 units down?
Solution:
From the given figure,
C = (-3, 2)
D = (2, 2)
Translation of the line segment by 4 units left and 5 units down.
So, subtract 4 from the x-coordinates and subtract 5 from the y-coordinates.
Thus, new coordinates will be:
C(-3, 2) = (-3 – 4, 2 – 5) = (-7, -3)
D(2, 2) = (2 – 4, 2 – 5) = (-2, -3)
8. Translate the following figure by:
(i) 5 units right and 4 units down
(ii) 1 unit right and 4 units down for (i)
(iii) 6 units left and 6 units down for (ii)
Solution:
If you consider each square as 1 square unit, we can get the vertices of the triangle as:
(5, 2), (-2, -4) and (1, -6)
(i) Translation by 5 units right and 4 units down
So, the new vertices will be:
(5, 2) = (5 + 5, 2 – 4) = (10, -2)
(-2, -4) = (-2 + 5, -4 – 4) = (3, -8)
(1, -6) = (1 + 5, -6 – 4) = (6, -10)
(ii) Translation by 1 unit right and 4 units down
(10, -2) = (10 + 1, -2 – 4) = (11, -6)
(3, -8) = (3 + 1, -8 – 4) = (4, -12)
(1, -6) = (1 + 1, -6 – 4) = (2, -10)
(iii) 6 units left and 6 units down
(11, -6) = (11 – 6, -6 – 6) = (5, -12)
(4, -12) = (4 – 6, -12 – 6) = (-2, -18)
(2, -10) = (2 – 6, -10 – 6) = (-4, -16)
Hence, the translated triangles can be shown as follows:
9. Write the coordinates of the vertices of the polygon ABCDE after it is translated by 3 units left and 5 units up.
Solution:
The vertices of the given figure are:
A = (-3, 2)
B = (1, 2)
C = (3, -1)
D = (0, -3)
E = (-4, -3)
Translation by 3 units left and 5 units up.
That means subtract 3 from the x-coordinates and add 5 to the y-coordinates.
So, the new vertices will be:
A’ = (-3 – 3, 2 + 5) = (-6, 7)
B’ = (1 – 3, 2 + 5) = (-2, 7)
C’ = (3 – 3, -1 + 5) = (0, 4)
D’ = (0 – 3, -3 + 5) = (-3, 2)
E’ = (-4 – 3, -3 + 5) = (-7, 2)
10. Draw the translation of the following figure by 5 units left and 2 units up.
Solution:
The translation of the given figure by 5 units left and 2 units up, is given below.
Practice Questions on Translation
1. Write the rule of translation from the triangle DEF to the other triangle D’E’F’.
2. Write the translation vertices for the following triangle by 5 units left and 2 units up.
3. What is the translation rule for the following figure?
4. Write the coordinates of the points that form a new line segment with the translation of the given line segment by 7 units right and 3 units up.
5. Write the translation rule for A to B and B to C.
