Question

Use the image to answer the 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:

\[
(4, -1)
\]