Question

Raiph draws a triangle on the coordinate grid. Its vertices are at (7,-3), (4, -7), and (-1,5). He translates this triangle, 4 units up and 2 units to the left. What are the coordinates of the lowest vertex on the translated triangle?(1 point)
Responses

(6,-3)
(6,-3)

(2,6)
(2,6)

(2,-11)
(2,-11)

(2,-3)

Answer 1

To find the coordinates of the lowest vertex on the translated triangle, we first need to determine the original coordinates of the vertices after the translation:

The original vertices of the triangle are:
1. (7, -3)
2. (4, -7)
3. (-1, 5)

When Raiph translates the triangle 4 units up and 2 units to the left:
- Translating a point (x, y) 4 units up changes its y-coordinate: (x, y + 4)
- Translating a point (x, y) 2 units to the left changes its x-coordinate: (x - 2, y)

Let's apply the translation to each vertex:

1. For the vertex (7, -3):
\[
(7 - 2, -3 + 4) = (5, 1)
\]

2. For the vertex (4, -7):
\[
(4 - 2, -7 + 4) = (2, -3)
\]

3. For the vertex (-1, 5):
\[
(-1 - 2, 5 + 4) = (-3, 9)
\]

Now, we have the coordinates of the translated vertices:
1. (5, 1)
2. (2, -3)
3. (-3, 9)

To identify the lowest vertex, we compare the y-coordinates of the translated vertices:
- For (5, 1), the y-coordinate is 1.
- For (2, -3), the y-coordinate is -3.
- For (-3, 9), the y-coordinate is 9.

The lowest vertex among these is (2, -3).

Thus, the coordinates of the lowest vertex on the translated triangle are **(2, -3)**.