Question

The coordinates of a triangle are (0, 0), (3, 0), and (0, 4). The coordinates of the translated triangle are (1, 2), (4, 2), and (1, 6). Find the translation vector.

1,6
4,2
6,1
1,2

Answer 1

D: (1,2)

Explanation:

To find the translation vector, we need to determine the difference between corresponding coordinates of the original triangle and the translated triangle.

Let's denote the original triangle's vertices as A(0, 0), B(3, 0), and C(0, 4). The corresponding vertices of the translated triangle are A'(1, 2), B'(4, 2), and C'(1, 6).

To find the translation vector, we subtract the coordinates of each vertex in the original triangle from the coordinates of the corresponding vertex in the translated triangle.

Translation vector for point A:

x-component: 1 - 0 = 1

y-component: 2 - 0 = 2

Translation vector for point B:

x-component: 4 - 3 = 1

y-component: 2 - 0 = 2

Translation vector for point C:

x-component: 1 - 0 = 1

y-component: 6 - 4 = 2

Therefore, the translation vector is (1, 2).