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Question

Translate triangle ABC by 3 units to the left and 5 units down. Which of the following are the coordinates of new triangle A′B′C′?

(1 point)
Responses

A′(−1,2), B′(−3,−2), C′(2,0)
upper A prime left parenthesis negative 1 comma 2 right parenthesis ,  upper B prime left parenthesis negative 3 comma negative 2 right parenthesis ,  upper C prime left parenthesis 2 comma 0 right parenthesis

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

A′(7,0), B′(5,−4), C′(10,−2)
upper A prime left parenthesis 7 comma 0 right parenthesis ,  upper B prime left parenthesis 5 comma negative 4 right parenthesis ,  upper C prime left parenthesis 10 comma negative 2 right parenthesis

A′(1,10), B′(−1,6), C′(4,7)

Answer 1

To find the coordinates of triangle A′B′C′ after translating triangle ABC by 3 units to the left and 5 units down, we need to adjust the coordinates of each vertex of triangle ABC accordingly.

Let's denote the original coordinates of points A, B, and C as \( (x_A, y_A) \), \( (x_B, y_B) \), and \( (x_C, y_C) \). The translation transforms these points as follows:

• Move 3 units to the left: This means we subtract 3 from the x-coordinates.
• Move 5 units down: This means we subtract 5 from the y-coordinates.

The new coordinates will be calculated as:

• \( A' = (x_A - 3, y_A - 5) \)
• \( B' = (x_B - 3, y_B - 5) \)
• \( C' = (x_C - 3, y_C - 5) \)

Since we do not have the original coordinates of triangle ABC provided, we cannot calculate the specific new coordinates, but we can evaluate the given response options against the translation rules.

To check each option:

1. A′(−1,2), B′(−3,−2), C′(2,0): We cannot verify without original coordinates.

2. A′(1,0), B′(−1,−4), C′(4,−2): We cannot verify without original coordinates.

3. A′(7,0), B′(5,−4), C′(10,−2): We cannot verify without original coordinates.

4. A′(1,10), B′(−1,6), C′(4,7): We cannot verify without original coordinates.

To find the correct response, you would need to know the original positions of A, B, and C. If you input those original coordinates, we could then calculate the new positions and identify the correct option. Without the original coordinates, we cannot determine which option is correct. Please provide the original coordinates if available.

Answer 2

well the original cords are A 5, 4 B 1, 2 C 3, 7

Answer 3

Given the original coordinates of the triangle ABC:

• A(5, 4)
• B(1, 2)
• C(3, 7)

We will apply the translation of 3 units to the left and 5 units down.

The new coordinates for each point after the translation are calculated as follows:

1. For point A (5, 4): \[ A' = (5 - 3, 4 - 5) = (2, -1) \]

2. For point B (1, 2): \[ B' = (1 - 3, 2 - 5) = (-2, -3) \]

3. For point C (3, 7): \[ C' = (3 - 3, 7 - 5) = (0, 2) \]

So, the new coordinates of triangle A′B′C′ are:

• A′(2, -1)
• B′(-2, -3)
• C′(0, 2)

Now, let's check against the provided options:

1. A′(−1,2), B′(−3,−2), C′(2,0): Not a match.

2. A′(1,0), B′(−1,−4), C′(4,−2): Not a match.

3. A′(7,0), B′(5,−4), C′(10,−2): Not a match.

4. A′(1,10), B′(−1,6), C′(4,7): Not a match.

None of the given options match the calculated new coordinates A′(2, -1), B′(-2, -3), and C′(0, 2).

If there's any mistake in calculation or if the options provided are incorrect, please verify and let me know how to assist further!