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

Question

(1 point)
Responses

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

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

Answer 1

To translate quadrilateral ADCB 5 units to the left and 2 units down, we need to adjust the coordinates of each vertex accordingly.

The steps to determine the new coordinates (A′D′C′B′) from the original coordinates (ADCB) are as follows:

1. Move 5 units to the left: This involves subtracting 5 from the x-coordinate of each vertex.
2. Move 2 units down: This involves subtracting 2 from the y-coordinate of each vertex.

If we denote the original coordinates of the points as:

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

The new coordinates will be:

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

Since we don’t have the original coordinates provided for A, D, C, and B, we cannot compute the new coordinates directly. However, we can evaluate the provided responses to determine which one is consistent with a 5-unit left and 2-unit down translation.

Now, just examine each provided answer in terms of what you would expect based on that transformation defined above.

Responses:

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

To check against a transformation of the form (x - 5, y - 2), the remaining coordinates will yield negative x-values for the new positions. Based on examining typical transformations characterized by shifting quadrilaterals:

Correct Response:

Given the nature of shifting left negatively on the x and downward on the y axis, typically points yielding positive would not align with a left shift. Hence, notice that standard transformation follows through through comparative vectors.

If original coordinates assume non-negativity contiguous through origin, access to quadrants 1-4 respectively adheres to the constraints necessitated building the deductions uniquely specified.

Without original coordinates, we cannot take precedence on identifying accurately. However, responses yielding deviation from negativity in x = 9 to respective movements yield clear contrast with expected translation.

In conclusion, if the original coordinates were in the range of fewer than 5, a likelihood towards left could yield a negative value less than 0. Please specify upon any particular coordinates to articulate upon verifiable results. Otherwise, the expectation leads towards a definitive option organically matched through translations discussed.