Question

select the correct answer.

triangle abc is translated 2 units right and 5 units down to form triangle abc. this triangle is then translated 5 units right and 4 units up to form triangle a\b\c\. if vertex a is at (-4, 2), what are the coordinates of vertex a\?

(3, -1)
(3, 1)
(-4, -2)
(2, -4)
(-11, 1)

Explanation:

Identify the initial coordinates

We start with the initial coordinates of vertex \(A\).
The problem states that vertex \(A\) is located at:

$$A = (-4, 2)$$

Apply the first translation

The first translation moves the triangle 2 units right and 5 units down to form \(A'B'C'\).

• Moving 2 units right adds 2 to the x-coordinate.
• Moving 5 units down subtracts 5 from the y-coordinate.

Using the rules of Geometric Translations:

$$x' = -4 + 2 = -2$$

$$y' = 2 - 5 = -3$$

So, the coordinates of \(A'\) are:

$$A' = (-2, -3)$$

Apply the second translation

The second translation moves the triangle 5 units right and 4 units up to form \(A''B''C''\).

• Moving 5 units right adds 5 to the x-coordinate of \(A'\).
• Moving 4 units up adds 4 to the y-coordinate of \(A'\).

Using Coordinate Transformations:

$$x'' = -2 + 5 = 3$$

$$y'' = -3 + 4 = 1$$

So, the coordinates of \(A''\) are:

$$A'' = (3, 1)$$

Answer:

• (3, -1)
• (3, 1) (Correct answer)
• (-4, -2)
• (2, -4)
• (-11, 1)