Question

Jaydin draws a triangle on the coordinate grid. Its vertices are at (−4,3), (−1,−5), and (−2,6). 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)Responses(4,−3)left parenthesis 4 comma negative 3 right parenthesis(1,0)left parenthesis 1 comma 0 right parenthesis(0,1)left parenthesis 0 comma 1 right parenthesis(−2,8)

Answer 1

To find the new coordinates of the triangle's vertices after the translation, we start by determining the coordinates of the original vertices:

1. Vertex A: \((-4, 3)\)
2. Vertex B: \((-1, -5)\)
3. Vertex C: \((-2, 6)\)

The translation involves moving 5 units up and 2 units to the right. This means:

• To move up: add 5 to the y-coordinate.
• To move right: add 2 to the x-coordinate.

Now let's apply this translation to each vertex:

1. For Vertex A \((-4, 3)\):

   • New x-coordinate: \(-4 + 2 = -2\)
   • New y-coordinate: \(3 + 5 = 8\)
   • Translated Vertex A: \((-2, 8)\)

2. For Vertex B \((-1, -5)\):

   • New x-coordinate: \(-1 + 2 = 1\)
   • New y-coordinate: \(-5 + 5 = 0\)
   • Translated Vertex B: \((1, 0)\)

3. For Vertex C \((-2, 6)\):

   • New x-coordinate: \(-2 + 2 = 0\)
   • New y-coordinate: \(6 + 5 = 11\)
   • Translated Vertex C: \((0, 11)\)

Now, we list the new vertices after translation:

• Translated Vertex A: \((-2, 8)\)
• Translated Vertex B: \((1, 0)\)
• Translated Vertex C: \((0, 11)\)

Next, we need to determine which of these vertices is the lowest. The lowest vertex will have the smallest y-coordinate. Comparing the y-coordinates:

• \(8\) (A)
• \(0\) (B)
• \(11\) (C)

Clearly, the lowest vertex is Vertex B, which has a y-coordinate of \(0\).

Thus, the coordinates of the lowest vertex on the translated triangle are \((1, 0)\).

Therefore, the answer is: (1, 0).