Understanding Translation in Geometry

What is the translation rule for moving a point (x, y) to (x+3, y-2)?

• The translation rule is: (x, y) -> (x+3, y-2)

• (x, y) -> (x-2, y-3)

• (x, y) -> (x+2, y+3)

• (x, y) -> (x-3, y+2)

Translate the triangle with vertices A(1, 2), B(3, 4), and C(5, 1) using the rule (x, y) -> (x-1, y+2). What are the new coordinates?

• A'(1, 2), B'(3, 4), C'(5, 1)

• A'(0, 4), B'(2, 6), C'(4, 3)

• A'(1, 5), B'(3, 6), C'(5, 3)

• A'(0, 2), B'(2, 4), C'(4, 1)

Graph the translated shape of a square with vertices (0,0), (0,1), (1,1), and (1,0) after applying the translation (x, y) -> (x+2, y-3).

• (1,-1), (1,0), (2,0), (2,-1)

• (2,1), (2,2), (3,2), (3,1)

• (0,-3), (0,-2), (1,-2), (1,-3)

• The new vertices of the translated square are (2,-3), (2,-2), (3,-2), and (3,-3).

If a rectangle is translated 4 units to the right and 2 units down, what are the new coordinates of the vertex originally at (2, 3)?

• (4, 5)

• (6, 1)

• (2, 1)

• (6, 3)

Describe how to translate a circle centered at (0, 0) with a radius of 5 to a new center at (3, 4).

• The new center of the circle is (3, 4) with a radius of 10.

• The new center of the circle is (0, 0) with a radius of 5.

• The new center of the circle is (3, 0) with a radius of 10.

• The new center of the circle is (3, 4) with a radius of 5.

What is the effect of translating a geometric figure on its area and perimeter?

• The area and perimeter of a geometric figure remain unchanged when it is translated.

• The area and perimeter both change based on the direction of translation.

• The area decreases and the perimeter increases.

• The area increases while the perimeter remains the same.

Given the points P(2, 3) and Q(4, 5), apply the translation (x, y) -> (x+1, y-1) and find the new coordinates of P and Q.

• P' = (1, 4), Q' = (3, 6)

• P' = (3, 2), Q' = (5, 4)

• P' = (3, 4), Q' = (5, 6)

• P' = (2, 3), Q' = (4, 5)

If a line segment connects points (1, 1) and (4, 4), what are the coordinates of the endpoints after a translation of (x, y) -> (x-2, y+3)?

• (0, 3) and (3, 6)

• (1, 1) and (4, 4)

• (-2, 1) and (1, 4)

• The new endpoints are (-1, 4) and (2, 7).

Solve the problem: A triangle with vertices at (2, 2), (3, 5), and (5, 3) is translated 3 units left and 1 unit up. What are the new coordinates?

• [[0, 3], [1, 6], [3, 4]]

• [[2, 2], [3, 5], [5, 3]]

• [[-1, 2], [0, 5], [2, 3]]

• [[-1, 3], [0, 6], [2, 4]]

Explain the process of graphing a translated figure step by step.

• Graphing a translated figure requires rotating the figure around a point.

• You must reflect the figure across the x-axis before graphing.

• Graphing a translated figure involves scaling the original figure by a factor.

• Graphing a translated figure involves applying a translation vector to each vertex of the original figure.