Translate shapes Draw the image of quadrilateral
under the translation
. 4 of
The Correct Answer and Explanation is:
✅ Correct Answer (Translated Coordinates):
You’re asked to translate quadrilateral ABCD under the rule: (x,y)→(x+4,y−3)(x, y) \rightarrow (x + 4, y – 3)
Let’s determine the coordinates of the original quadrilateral:
- A (0, 0)
- B (1, -4)
- C (-6, -2)
- D (-3, 1)
Now, apply the translation rule to each point:
- A′ = (0 + 4, 0 − 3) = (4, -3)
- B′ = (1 + 4, -4 − 3) = (5, -7)
- C′ = (-6 + 4, -2 − 3) = (-2, -5)
- D′ = (-3 + 4, 1 − 3) = (1, -2)
📝 300-Word Explanation:
A translation is a type of geometric transformation that moves every point of a figure the same distance in a specified direction. In this problem, we apply the translation rule (x,y)→(x+4,y−3)(x, y) \rightarrow (x + 4, y – 3), which means moving the shape 4 units right and 3 units down on the coordinate plane.
To translate a shape, we apply the rule to each of its vertices. For instance, the original point A is at (0, 0). When we add 4 to the x-coordinate and subtract 3 from the y-coordinate, we get A′ at (4, -3). We do the same for all other points: B, C, and D. This ensures that the entire shape moves uniformly without changing its size, shape, or orientation.
After applying the rule, we get a new quadrilateral A′B′C′D′. The shape remains congruent to the original because a translation is a rigid motion, which preserves distances and angles. Essentially, the figure is “slid” from one place to another without any rotation or flipping.
Translations are widely used in computer graphics, animation, robotics, and real-life navigation systems, where maintaining the structure of an object while repositioning it is essential.
In conclusion, translating shapes on a coordinate plane is a simple yet powerful concept in geometry. It reinforces the idea of spatial awareness, symmetry, and congruence, all while helping develop a deeper understanding of how figures behave under transformation.
