Question

Jaydin draws a triangle on the coordinate grid. Its vertices are at (−4,3)%0D%0A(%0D%0A−%0D%0A4%0D%0A,%0D%0A3%0D%0A)%0D%0A, (−1,−5)%0D%0A(%0D%0A−%0D%0A1%0D%0A,%0D%0A−%0D%0A5%0D%0A)%0D%0A, and (−2,6)%0D%0A(%0D%0A−%0D%0A2%0D%0A,%0D%0A6%0D%0A)%0D%0A. He translates this triangle 5 units up and 2 units to the right. What are the coordinates of the lowest vertex on the translated triangle?(1 point)%0D%0AResponses%0D%0A%0D%0A(1,0)%0D%0A(%0D%0A1%0D%0A,%0D%0A0%0D%0A)%0D%0Aleft parenthesis 1 comma 0 right parenthesis%0D%0A%0D%0A(−2,8)%0D%0A(%0D%0A−%0D%0A2%0D%0A,%0D%0A8%0D%0A)%0D%0Aleft parenthesis negative 2 comma 8 right parenthesis%0D%0A%0D%0A(4,−3)%0D%0A(%0D%0A4%0D%0A,%0D%0A−%0D%0A3%0D%0A)%0D%0Aleft parenthesis 4 comma negative 3 right parenthesis%0D%0A%0D%0A(0,1)

Answer 1

To find the coordinates of the lowest vertex on the translated triangle, we first identify the original vertices and then apply the translation.

The original vertices of the triangle are:
1. \((-4, 3)\)
2. \((-1, -5)\)
3. \((-2, 6)\)

Next, we apply the translation: moving the triangle 5 units up and 2 units to the right means we add 2 to the x-coordinates and 5 to the y-coordinates of each vertex.

Let’s calculate the translated coordinates:

1. For \((-4, 3)\):
\[
x = -4 + 2 = -2 \\
y = 3 + 5 = 8 \\
\text{Translated vertex: } (-2, 8)
\]

2. For \((-1, -5)\):
\[
x = -1 + 2 = 1 \\
y = -5 + 5 = 0 \\
\text{Translated vertex: } (1, 0)
\]

3. For \((-2, 6)\):
\[
x = -2 + 2 = 0 \\
y = 6 + 5 = 11 \\
\text{Translated vertex: } (0, 11)
\]

Now we have the translated vertices:
- \((-2, 8)\)
- \((1, 0)\)
- \((0, 11)\)

To find the lowest vertex, we compare the y-coordinates:
- For \((-2, 8)\), the y-coordinate is 8.
- For \((1, 0)\), the y-coordinate is 0.
- For \((0, 11)\), the y-coordinate is 11.

The lowest y-coordinate is 0, which corresponds to the vertex at \((1, 0)\).

Thus, the coordinates of the lowest vertex on the translated triangle are:
\[
\boxed{(1, 0)}
\]