QuestionA 5 T B C -3 E -2 2 D Find the composition of transformations that map ABCD to EHGF. Reflect over the [?]-axis, then translate (x+[ ], y+[ ]). 0 2 3 F Note: -2 G Enter x or y for axis
Studdy Solution
STEP 1
1. Quadrilateral ABCD is initially positioned above the x-axis.
2. Quadrilateral EHGF is positioned below the x-axis.
3. The transformation involves a reflection over an axis and a translation.
STEP 2
1. Determine the axis of reflection.
2. Reflect quadrilateral ABCD over the determined axis.
3. Determine the translation vector.
4. Translate the reflected quadrilateral to map onto EHGF.
STEP 3
Determine the axis of reflection:
- Observe the y-coordinates of corresponding points in ABCD and EHGF.
- Points A and E have y-coordinates 2 and -2, respectively.
- Points B and H have y-coordinates 5 and -3, respectively.
- Points C and G have y-coordinates 5 and -3, respectively.
- Points D and F have y-coordinates 2 and -2, respectively.
The reflection occurs over the x-axis, as the y-coordinates of corresponding points are negations.
STEP 4
Reflect quadrilateral ABCD over the x-axis:
- Reflect each vertex of ABCD over the x-axis:
- A(-5, 2) becomes A'(-5, -2)
- B(-3, 5) becomes B'(-3, -5)
- C(0, 5) becomes C'(0, -5)
- D(-2, 2) becomes D'(-2, -2)
STEP 5
Determine the translation vector:
- Compare the reflected coordinates with EHGF:
- A'(-5, -2) to E(-5, -2)
- B'(-3, -5) to H(-3, -3)
- C'(0, -5) to G(0, -3)
- D'(-2, -2) to F(2, -2)
- Notice that the x-coordinates of D' and F differ by 4 units (from -2 to 2).
The translation vector is (x + 4, y + 0).
STEP 6
Translate the reflected quadrilateral:
- Apply the translation vector (x + 4, y + 0) to each reflected vertex:
- A'(-5, -2) becomes E(-5, -2) (no change needed)
- B'(-3, -5) becomes H(-3, -3) (translate up by 2 units)
- C'(0, -5) becomes G(0, -3) (translate up by 2 units)
- D'(-2, -2) becomes F(2, -2) (translate right by 4 units)
The composition of transformations is:
1. Reflect over the x-axis.
2. Translate by (x + 4, y + 0).
Was this helpful?
