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Question

A coordinate plane's x-axis ranges from negative 3 to 9 and its y-axis ranges from negative 2 to 6, both by 1-unit increments. 3 points are marked and plotted forming triangle upper A upper B upper C.

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)
upper A prime left parenthesis 1 comma 10 right parenthesis , upper B prime left parenthesis negative 1 comma 6 right parenthesis , upper C prime left parenthesis 4 comma 7 right parenthesis
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Answer 1

To translate triangle ABC by 3 units to the left and 5 units down, we need to adjust the coordinates of each vertex of the triangle (A, B, C) as follows:

• For a left translation of 3 units: subtract 3 from the x-coordinate.
• For a downward translation of 5 units: subtract 5 from the y-coordinate.

If the original coordinates of the triangle are:

• A(x_A, y_A)
• B(x_B, y_B)
• C(x_C, y_C)

The coordinates after translation will be:

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

To determine the new coordinates, we would need the original coordinates of points A, B, and C, which are not provided in your question. However, let's take a look at the options given and apply the translation to find if any of them fit:

1. A′(−1,2), B′(−3,−2), C′(2,0)
2. A′(1,0), B′(−1,−4), C′(4,−2)
3. A′(7,0), B′(5,−4), C′(10,−2)
4. A′(1,10), B′(−1,6), C′(4,7)

We would need the original coordinates of triangle ABC to compute the translated coordinates and verify which option is correct. If you provide those original coordinates, I can help you compute the translated coordinates directly.