Question

Use the image to answer the question.

A coordinate plane shows all four quadrants with both axes ranging from negative 7 to 7 in increments of 1. A right triangle is graphed on quadrant 2. Three points labeled as upper A, upper B, and upper C are plotted at coordinates left parenthesis negative 1 comma 1 right parenthesis, left parenthesis negative 1 comma 6 right parenthesis, and left parenthesis negative 5 comma 1 right parenthesis, respectively. The three points are joined by solid lines to form triangle upper A upper B upper C whose base is upper A upper C, hypotenuse is upper B upper C, and perpendicular side is upper A upper B.

What are the values of the coordinates for point B′ after right triangle ABC has been translated 2 units to the right and 4 units down?

(1 point)
B′(
,
)
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Answer 1

[AI-generated answer — Bot GPT 3.5]

B′(1, 2)

Answer 2

Use the image to answer the question.

A coordinate plane shows all four quadrants with both axes ranging from negative 8 to 8 in increments of 1. Two right triangles are graphed on the plane. Three points labeled as upper D, upper E, and upper F are plotted at coordinates left parenthesis negative 6 comma negative 5 right parenthesis, left parenthesis negative 6 comma negative 2 right parenthesis, and left parenthesis negative 3 comma negative 5 right parenthesis, respectively. The three points are joined by solid lines to form triangle upper D upper E upper F whose base is upper D upper F, hypotenuse is upper E upper F, and perpendicular side is upper D upper E. Three other points labeled as upper D prime, upper E prime, and upper F prime are plotted at coordinates left parenthesis negative 1 comma negative 7 right parenthesis, left parenthesis negative 1 comma negative 4 right parenthesis, and left parenthesis 2 comma negative 7 right parenthesis, respectively. These three points are joined by dotted lines to form triangle upper D prime upper E prime upper F prime whose base is upper D prime upper F prime, hypotenuse is upper E prime upper F prime, and perpendicular side is upper D prime upper E prime.

What is the value of the horizontal translation that occurs?

(1 point)
units
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Answer 3

[AI-generated answer — Bot GPT 3.5]

4 units

Answer 4

wrong

Answer 5

[AI-generated answer — Bot GPT 3.5]

I apologize for the error. Let's find the correct horizontal translation that occurs:

Point D has coordinates (-6, -5) and point D' has coordinates (-1, -7). To find the horizontal translation, we need to find the difference in x-coordinates between D and D'.

D' is to the right of D, so the translation will be positive.

Horizontal translation = x-coordinate of D' - x-coordinate of D
Horizontal translation = -1 - (-6)
Horizontal translation = -1 + 6
Horizontal translation = 5 units

Therefore, the correct horizontal translation that occurs is 5 units.