Answer:
(A) The rule for the translation can be written as T–3, 1(x, y)
(D) The rule for the translation can be written as (x, y) → (x – 3, y + 1)
The complete question related to this found on brainly(ID: 14843069 ) is stated below:
On a coordinate plane, 2 trapezoids are shown. The first trapezoid has points A (negative 1, negative 2), B (1, negative 2), C (2, negative 5), and D (negative 2, negative 5). The second trapezoid has points A prime (negative 4, negative 1), B prime (negative 2, negative 1), C prime (negative 1, negative 4), and D prime (negative 5, negative 4).
Which statements are true about trapezoid ABCD and its translated image, A'B'C'D'? Select two options.
A) The rule for the translation can be written as T–3, 1(x, y).
B) The rule for the translation can be written as T–1, 3(x, y).
C) The rule for the translation can be written as (x, y) → (x + 1, y – 3).
D) The rule for the translation can be written as (x, y) → (x – 3, y + 1).
Trapezoid ABCD has been translated 3 units to the right and 1 unit up.
Step-by-step explanation:
Vertices of trapezoid ABCD
A(-1, -2) B(1, -2) C(2, -5) D(-2, -5)
Vertices of trapezoid A'B'C'D'
A'(-4, -1) B'(-2, -1) C'(-1, -4) D'(-5, -4)
Trapezoid ABCD has been translated 3 units to the right and 1 unit up.
From the rule of translation:
A point (x , y) translated horizontally to the right by h units would have its image as: (x + h , y)
A point (x , y) translated vertically up by k units would have its image as (x , y + k)
The original figure, trapezoid ABCD was translated to form new image, trapezoid A'B'C'D'. We would determine the right statements using any corresponding coordinates in both trapezoid as they would give same result.
Using B coordinates and B' coordinates: B = (1, -2) and A' = (-2, -1)
(1, -2) → (-2, -1)
Translation is from (x , y) → (x+h, y+k)
x = -1, x + h = -4
x + h = -4 (insert value of x)
-1 + h = -4
h = -4+1
h = -3
y = -2, x + h = -1
y + k = -1 (insert value of y)
-2 + k = -1
k = -1+2
k = 1
The rule of translation is (x , y) → (x +(-3), y + 1) = (x , y) → (x-3, y+1)
From the above, we can say the trapezoid ABCD has been translated 3 units to the left and 1 unit up
Correct statements:
(A) The rule for the translation can be written as T–3, 1(x, y)
(D) The rule for the translation can be written as (x, y) → (x – 3, y + 1)
