Question

The vertices MNPQ are M(-4,1), N(-2,4), P(2,3), and Q(1, -3) Translate quadrilateral MNPQ using the vector (2,-3).

Answer 1

To translate quadrilateral MNPQ by the vector (2, -3), each vertex is moved 2 units right and 3 units down, resulting in the new vertices M'(-2, -2), N'(0, 1), P'(4, 0), and Q'(3, -6).

Step-by-step explanation:

To translate quadrilateral MNPQ using the vector (2, -3), we simply need to add the vector components to each of the vertices' coordinates.

• The new position of M, M' is (-4 + 2, 1 - 3), which is (-2, -2).
• The new position of N, N' is (-2 + 2, 4 - 3), which is (0, 1).
• The new position of P, P' is (2 + 2, 3 - 3), which is (4, 0).
• The new position of Q, Q' is (1 + 2, -3 - 3), which is (3, -6).

The quadrilateral MNPQ has been translated to the new quadrilateral M'N'P'Q' with vertices at (-2, -2), (0, 1), (4, 0), and (3, -6) respectively.