Use the image to answer the question.

Question

Linda draws a triangle on the coordinate grid with vertices at (1,2)
(
1
,
2
)
, (3,−4)
(
3
,
−
4
)
, and (7,0)
(
7
,
0
)
. She translates this triangle 3 units to the left and 1 unit down. What are the coordinates of the rightmost vertex on her translated triangle?

(1 point)
(,)

Answer 1

To find the new coordinates of the triangle vertices after the translation, we need to subtract 3 units from the x-coordinates (to move left) and subtract 1 unit from the y-coordinates (to move down).

The original coordinates of the vertices are:

• (1, 2)
• (3, -4)
• (7, 0)

Let's translate each vertex:

1. For the vertex (1, 2): \[ x' = 1 - 3 = -2 \] \[ y' = 2 - 1 = 1 \] New coordinates: \((-2, 1)\)

2. For the vertex (3, -4): \[ x' = 3 - 3 = 0 \] \[ y' = -4 - 1 = -5 \] New coordinates: \((0, -5)\)

3. For the vertex (7, 0): \[ x' = 7 - 3 = 4 \] \[ y' = 0 - 1 = -1 \] New coordinates: \((4, -1)\)

Now, let's identify the rightmost vertex among the translated coordinates:

• \((-2, 1)\)
• \((0, -5)\)
• \((4, -1)\)

The x-coordinate of the rightmost vertex is the largest, which is \(4\).

Thus, the coordinates of the rightmost vertex on her translated triangle are:

\[ (4, -1) \]