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?

a. (2, 6)
b. (2, -3)
c. (2, -11)
d. (6, -3)

Answer 1

To find the coordinates of the lowest vertex on the translated triangle, we first identify the lowest vertex of the original triangle.

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

To find the lowest vertex, we need to consider the y-coordinates of these points:
- (7, -3) has a y-coordinate of -3
- (4, -7) has a y-coordinate of -7
- (-1, 5) has a y-coordinate of 5

The lowest y-coordinate among these is -7, which corresponds to the vertex (4, -7).

Now we will translate this vertex 4 units up and 2 units to the left.
- Moving 4 units up means we add 4 to the y-coordinate:
\(-7 + 4 = -3\)
- Moving 2 units to the left means we subtract 2 from the x-coordinate:
\(4 - 2 = 2\)

Thus, the coordinates of the translated vertex are (2, -3).

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

The correct answer is:
**b. (2, -3)**