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

(−2,8)
left parenthesis negative 2 comma 8 right parenthesis

(0,1)

Answer 1

Let's first identify the vertices of the triangle:

1. \(A (-4, 3)\)
2. \(B (-1, -5)\) (this is the lowest vertex)
3. \(C (-2, 6)\)

Next, we need to translate each vertex of the triangle 5 units up and 2 units to the right.

**Translation Steps:**
- To translate a point (x, y), you add 2 to the x-coordinate and 5 to the y-coordinate.
- New coordinates = \((x + 2, y + 5)\)

Now, let's apply the translation to each vertex:

1. For vertex \(A (-4, 3)\):
\[
A' = (-4 + 2, 3 + 5) = (-2, 8)
\]

2. For vertex \(B (-1, -5)\):
\[
B' = (-1 + 2, -5 + 5) = (1, 0)
\]

3. For vertex \(C (-2, 6)\):
\[
C' = (-2 + 2, 6 + 5) = (0, 11)
\]

The lowest vertex before translation was \(B (-1, -5)\), and after translation, the new coordinates are \(B' (1, 0)\).

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