To translate a quadrilateral by a certain distance, you add the translation values to each of the original coordinates of the vertices.
Let's denote the original coordinates of quadrilateral ABCD as:
- A(x₁, y₁)
- B(x₂, y₂)
- C(x₃, y₃)
- D(x₄, y₄)
For this translation, we need to:
- Move right by 2 units: Add 2 to the x-coordinates.
- Move up by 4 units: Add 4 to the y-coordinates.
The new coordinates after the translation will be:
- A′(x₁ + 2, y₁ + 4)
- B′(x₂ + 2, y₂ + 4)
- C′(x₃ + 2, y₃ + 4)
- D′(x₄ + 2, y₄ + 4)
From the options provided, we need to identify which set of coordinates corresponds to this transformation.
Now, let’s evaluate the four given options for the expected coordinates.
Option 1:
- A′(7,−1), B′(10,1), C′(12,−1), D′(10,−3)
Option 2:
- A′(3,7), B′(6,9), C′(8,7), D′(6,5)
Option 3:
- A′(3,−1), B′(6,1), C′(8,−1), D′(6,−3)
Option 4:
- A′(7,7), B′(10,9), C′(12,7), D′(10,5)
To find the transformed coordinates, we can deduce that:
If originally A is (x₁, y₁) then:
- A' = (x₁ + 2, y₁ + 4) For this to yield integer coordinates in the ranges given, we must apply the transformations.
Let's take one of the options and assume A' = (3, -1) and see if it satisfies the transformation conditions. If A′ = (3,−1):
- This means its original coordinates A might have been (1, 3) since (1 + 2, 3 + 4) = (3, -1).
However, let's evaluate which options have all corresponding transformations consistent across the quadrilateral.
At a glance:
- Option 3 seems to hold the right transformation under basic translation principles considering the vertical and horizontal scaling.
Thus, the answer is: Option 3: A′(3,−1), B′(6,1), C′(8,−1), D′(6,−3).
1 answer