Question
The vertices of △ 𝐴𝐵𝐶 are A (2, 4), B (1, 1), and C (5,1). A translation of △ 𝐴𝐵𝐶 results in the image △𝑃𝑄𝑅 with vertices P (3, 2), Q (2, -1), and R (6, -1). Describe the translation in words and in coordinate notation.
Hint:
Translation is displacement of an object.
The correct answer is: (x , y) (x + 1 , y – 2)
We know that in transformation by translation figure or shape is displaced from one place to another. A figure can move upward, downward, right, left or anywhere in the coordinate system but the size remains same.
Let the displacement along x – axis be ‘a’ and along y – axis be ‘b’.
A = P 
(2 + a , 4 + b) = (3, 2)
2 + a = 3 , 4 + b = 2
a = 1 , b = - 2
In translation, when a figure or shape is displaced every point of the figure is displaced by same units. So, we only need to solve for one point.
Hence, coordinate notation is (x , y) → (x + 1 , y – 2)
Related Questions to study
Use a reflection in the x – axis to draw the other half of the pattern.
Use a reflection in the x – axis to draw the other half of the pattern.
A field is in the shape of a trapezium whose parallel sides are 90m and 30m. These sides meet third side at right angle. The length of the fourth side is 100m.If it costs Rs 4 to ploughing the field. Find the total cost of ploughing the field.
A field is in the shape of a trapezium whose parallel sides are 90m and 30m. These sides meet third side at right angle. The length of the fourth side is 100m.If it costs Rs 4 to ploughing the field. Find the total cost of ploughing the field.
If angle A and angle B of △ ABC are congruent with corresponding angles X and Y of △
XYZ respectively, then
If angle A and angle B of △ ABC are congruent with corresponding angles X and Y of △
XYZ respectively, then
Use a reflection in the Y-axis to draw the other half of the pattern
Use a reflection in the Y-axis to draw the other half of the pattern
Identify the transformation and find the values of a and b.
Identify the transformation and find the values of a and b.
What is one possible solution to the equation above?
Note:
Instead of using the quadratic formula, we could also use middle term factorization to solve the quadratic equation 
in the following way:
Thus we get values of x = 2 or 3 .
What is one possible solution to the equation above?
Note:
Instead of using the quadratic formula, we could also use middle term factorization to solve the quadratic equation
in the following way:
Thus we get values of x = 2 or 3 .
(𝑥, 𝑦) → (−𝑥, 𝑦) represents
(𝑥, 𝑦) → (−𝑥, 𝑦) represents
Here, AD ∥ BC
Identify the congruent triangles and congruent corresponding parts. Write the congruence properties or theorems used.
Here, AD ∥ BC
Identify the congruent triangles and congruent corresponding parts. Write the congruence properties or theorems used.
Find the co-ordinates of an image of the point (-5, -8) after reflection about Y-axis
Find the co-ordinates of an image of the point (-5, -8) after reflection about Y-axis
A field is in the shape of a trapezium whose parallel sides are 25m and 10m. The non parallel sides are 14m and 13m, find the area.
A field is in the shape of a trapezium whose parallel sides are 25m and 10m. The non parallel sides are 14m and 13m, find the area.
Find the co-ordinates of an image of the point (1, 2) after reflection about X-axis.
Find the co-ordinates of an image of the point (1, 2) after reflection about X-axis.
Figure PQR has the vertices P (3, 3), Q (5, 5), R (8, 3). Find co-ordinates of its image ABC after the translation (x, y) → (x + 4, y - 4)
Figure PQR has the vertices P (3, 3), Q (5, 5), R (8, 3). Find co-ordinates of its image ABC after the translation (x, y) → (x + 4, y - 4)
Figure PQRS has the vertices P (14, 3), Q (12, 4), R (11, 3), and S (13, 2). Find co-ordinates of its image ABCD after the translation (x, y) → (x + 2, y - 5).
Figure PQRS has the vertices P (14, 3), Q (12, 4), R (11, 3), and S (13, 2). Find co-ordinates of its image ABCD after the translation (x, y) → (x + 2, y - 5).
△ ABC ≅△ PQR
AB = 10 ft, BC = 6 ft, AC = 6 ft
PQ = 2y, QR = x + 2, RS = 2x − 2
Find the values of x and y.
△ ABC ≅△ PQR
AB = 10 ft, BC = 6 ft, AC = 6 ft
PQ = 2y, QR = x + 2, RS = 2x − 2
Find the values of x and y.
In the equation above, what is the value of s when t= -1 ?
Note:
Instead of adding 1 on both sides, we can also understand the concept by taking _1 of the left hand side on the right hand side and then the sign changes to +1 . Similarly, instead of dividing by 2, we can understand it by saying that we take 2 from the left hand side to the right hand side, and here it becomes division.
Thus, addition becomes subtraction and vice-versa when taken from left hand side to right hand side or the opposite way; and multiplication becomes division and vice-versa. Be careful, 0 is never taken in the denominator.
In the equation above, what is the value of s when t= -1 ?
Note:
Instead of adding 1 on both sides, we can also understand the concept by taking _1 of the left hand side on the right hand side and then the sign changes to +1 . Similarly, instead of dividing by 2, we can understand it by saying that we take 2 from the left hand side to the right hand side, and here it becomes division.
Thus, addition becomes subtraction and vice-versa when taken from left hand side to right hand side or the opposite way; and multiplication becomes division and vice-versa. Be careful, 0 is never taken in the denominator.
