Use the image to answer the question.

Question

Translate quadrilateral ADCB 5 units to the left and 2 units down. What are the coordinates of new quadrilateral A′D′C′B′?

(1 point)
Responses

A′(−1,0), D′(−1,5), C′(4,2), B′(2,−1)
upper A prime left parenthesis negative 1 comma 0 right parenthesis , upper D prime left parenthesis negative 1 comma 5 right parenthesis , upper C prime left parenthesis 4 comma 2 right parenthesis , upper B prime left parenthesis 2 comma negative 1 right parenthesis

A′(9,−4), D′(9,1), C′(13,−2), B′(12,−5)
upper A prime left parenthesis 9 comma negative 4 right parenthesis , upper D prime left parenthesis 9 comma 1 right parenthesis , upper C prime left parenthesis 13 comma negative 2 right parenthesis , upper B prime left parenthesis 12 comma negative 5 right parenthesis

A′(9,0), D′(9,5), C′(13,2), B′(12,−1)
upper A prime left parenthesis 9 comma 0 right parenthesis , upper D prime left parenthesis 9 comma 5 right parenthesis , upper C prime left parenthesis 13 comma 2 right parenthesis , upper B prime left parenthesis 12 comma negative 1 right parenthesis

A′(−1,−4), D′(−1,1), C′(4,−2), B′(2,−5)

Answer 1

To translate quadrilateral ADCB 5 units to the left and 2 units down, you subtract 5 from the x-coordinates and subtract 2 from the y-coordinates of each vertex.

Let’s define the original coordinates of points A, D, C, and B:

• A(x₁, y₁)
• D(x₂, y₂)
• C(x₃, y₃)
• B(x₄, y₄)

The new coordinates after translation will be:

• A′(x₁ - 5, y₁ - 2)
• D′(x₂ - 5, y₂ - 2)
• C′(x₃ - 5, y₃ - 2)
• B′(x₄ - 5, y₄ - 2)

Unfortunately, I cannot see the original image or coordinates you are referring to, but you can plug in the values from your quadrilateral ADCB to find A′, D′, C′, and B′.

From the choices provided:

1. A′(−1,0), D′(−1,5), C′(4,2), B′(2,−1)
2. A′(9,−4), D′(9,1), C′(13,−2), B′(12,−5)
3. A′(9,0), D′(9,5), C′(13,2), B′(12,−1)
4. A′(−1,−4), D′(−1,1), C′(4,−2), B′(2,−5)

You should calculate the new coordinates based on the original ones given by the image, and compare them to these options to find the correct answer. If you have more information or the original coordinates, feel free to share and I can help you verify which option is correct!