Question

Translate the given AABC along the vector PQ.

B
-543
C
H
5+
4
3
2
1
-1
-2
-3
A
4
-5+
1 2 3 4
P
5
X
Q

Answer 1

The translated triangle A'B'C' is formed by the vertices A'(6, 9), B'(9, 13), and C'(12, 9).

To translate a triangle along a vector, we can apply the translation to each vertex of the triangle.

Triangle ABC has vertices A(2, 3), B(5, 7), and C(8, 3). The vector PQ is represented by the coordinates (4, 6).

The translation of a point (x, y) along the vector (a, b) can be done using the formula:

`\[ (x', y') = (x + a, y + b) \]`

Now, apply this formula to each vertex of the triangle:

1. For vertex A(2, 3):

`\[ A'(x', y') = (2 + 4, 3 + 6) = (6, 9) \]`

2. For vertex B(5, 7):

`\[ B'(x', y') = (5 + 4, 7 + 6) = (9, 13) \]`

3. For vertex C(8, 3):

`\[ C'(x', y') = (8 + 4, 3 + 6) = (12, 9) \]`

So, the translated triangle A'B'C' is formed by the vertices A'(6, 9), B'(9, 13), and C'(12, 9).

The probable question may be:

"Translate the given triangle ABC along the vector PQ where triangle ABC has vertices A(2, 3), B(5, 7), and C(8, 3). The vector PQ is represented by the coordinates (4, 6)"