Question

Triangle ABC has coordinates

A
(
2
,
0
)
,
B
(
−
1
,
5
)
,
and
C
(
4
,
3
)
.
Determine the coordinates of the vertices of the image after a translation along the vector 〈3, –4〉.

Answer 1

Vertex A: (5, -4)

Vertex B: (2, 1)

Vertex C: (7, -1)

Explanation:

Let's calculate the new coordinates for each vertex:

Vertex A: (2, 0) + (3, -4) = (2 + 3, 0 - 4) = (5, -4)

Vertex B: (-1, 5) + (3, -4) = (-1 + 3, 5 - 4) = (2, 1)

Vertex C: (4, 3) + (3, -4) = (4 + 3, 3 - 4) = (7, -1)

Therefore, the coordinates of the vertices of the image after the translation along the vector 〈3, –4〉 are:

Vertex A: (5, -4)

Vertex B: (2, 1)

Vertex C: (7, -1)