Question

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.


The rule for the translation can be written as T–3, 1(x, y).

The rule for the translation can be written as T–1, 3(x, y).

The rule for the translation can be written as

(x, y) → (x + 1, y – 3).

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.

ANSWER :
~ The rule for the translation can be written as T-3, 1(x, y).
~ The rule for the translation can be written as
(x, y) → (x - 3, y + 1).

Answer 1

Answer:

The true statements are:

The rule for the translation can be written as T-3, 1(x, y). ⇒ 1st

The rule for the translation can be written as  (x, y) → (x - 3, y + 1) ⇒ 4th

Step-by-step explanation:

Let us revise the rule of the translation:

• If the point (x , y) translated horizontally to the right by h units  then its image is (x + h , y)
• If the point (x , y) translated horizontally to the left by h units  then its image is (x - h , y)
• If the point (x , y) translated vertically up by k units  then its image is (x , y + k)
• If the point (x , y) translated vertically down by k units  then its image is (x , y - k)

The vertices of trapezoid ABCD are:

A (-1 , -2) , B (1 , -2) , C (2 , -5) , D (-2 , -5)

The vertices Of trapezoid A'B'C'D' are:

A' (-4 , -1) , B' (-2 , -1) , C' (-1 , -4) , D' (-5 , -4)

Trapezoid ABCD is translated to form Trapezoid A'B'C'D'

By using the rules of translation above:

∵ A = (-1 , -2) and A' = (-4 , -1)

- The rule of translation is (x , y) → (x + h , y + k)

∵ x = -1 and x + h = -4

∴ -1 + h = -4

- Add 1 to both sides

∴ h = -3

∵ y = -2 and y + k = -1

∴ -2 + k = -1

- Add 2 to both sides

∴ k = 1

The rule of translation is (x , y) → (x - 3 , y + 1)

The trapezoid ABCD has been translated 3 units to the left and 1 unit  up

You can check your answer by doing the same steps with the other 3 vertices you will have the same values of h and k

The true statements are:

The rule for the translation can be written as T-3, 1(x, y).

The rule for the translation can be written as  (x, y) → (x - 3, y + 1)

Answer 2

Answer:

A,D

Step-by-step explanation:

I took the test on E2020.