19 or 20. Describe the sequence of transformations from quadrilateral ABCD to A’B’C’D’.
The graph is 10 by 10 (the x and y coordinates go to 10 and negative 10 at maximum). A is at -8,8 B is at -2,8, C is at -8,4 and D is at -2,4.
A' is at 2,-10 B' is at 8,-10 C' is at 2,-6 and D' is at 8,-6.
I know that it's at least a reflection (flip) over the X-axis, but that's all I got. Help, please!
Well, buckle up, because this quadrilateral is about to go through a wild transformation sequence! It's like quadrilateral ABCD is going to a circus and you're in for a clown-tastic show!
First off, let's start with a reflection over the x-axis. This means that the entire quadrilateral gets flipped upside down, just like a clown doing a somersault! So now you have a new quadrilateral with A at -8,-8, B at -2,-8, C at -8,-4, and D at -2,-4. Let's call this ABCD prime!
But hold on tight, because there's more to come! Next, we need to perform a translation. We're going to slide the quadrilateral 10 units to the right, just like a clown sneaking up on someone. So now we have a new quadrilateral, A'B'C'D'!
Let's see where our clown quadrilateral ended up: A' is at -8,-8 + 10 = 2,-10, B' is at -2,-8 + 10 = 8,-10, C' is at -8,-4 + 10 = 2,-6, and D' is at -2,-4 + 10 = 8,-6.
And voila! Quadrilateral ABCD transformed into A'B'C'D' through a reflection over the x-axis and then a translation 10 units to the right. It's like the quadrilateral joined the circus and turned into a whole new act!
I hope this helps you visualize the transformation sequence. And hey, if you need any more clown-worthy explanations, you know where to find me!
To transform quadrilateral ABCD to A’B’C’D’, it involves a series of transformations. The given vertices of ABCD and A’B’C’D’ are as follows:
ABCD: A(-8, 8), B(-2, 8), C(-8, 4), D(-2, 4)
A’B’C’D’: A’(2, -10), B’(8, -10), C’(2, -6), D’(8, -6)
The sequence of transformations to perform is:
1. Reflection over the X-axis:
Reflect each point of ABCD across the X-axis to obtain A(-8, -8), B(-2, -8), C(-8, -4), D(-2, -4).
2. Translation along the Y-axis:
Move each point of ABCD vertically downward by 10 units to obtain A(-8, -18), B(-2, -18), C(-8, -14), D(-2, -14).
3. Reflection over the X-axis:
Reflect each point of the translated ABCD across the X-axis to obtain A(8, -18), B(2, -18), C(8, -14), D(2, -14).
4. Translation along the X-axis:
Move each point of the reflected ABCD horizontally rightward by 10 units to obtain A’(2, -10), B’(8, -10), C’(2, -6), D’(8, -6), which are the vertices of A’B’C’D’.
So, the sequence of transformations from quadrilateral ABCD to A’B’C’D’ is:
- Reflection over the X-axis
- Translation along the Y-axis
- Reflection over the X-axis
- Translation along the X-axis.
To describe the sequence of transformations from the quadrilateral ABCD to A'B'C'D', we will break it down step by step based on the given information.
1. Reflection over the X-axis:
The given points of ABCD have positive y-coordinates, while the points of A'B'C'D' have negative y-coordinates. This indicates a reflection over the X-axis.
Applying the reflection over the X-axis to the points of ABCD would result in A=(-8, -8), B=(-2, -8), C=(-8, -4), and D=(-2, -4).
2. Translation of 10 units in the positive y-direction:
Looking at the transformation from A'B'C'D' to A''B''C''D'', we can observe that the y-coordinates of A'B'C'D' are -10 units less than A''B''C''D'.
By adding 10 units to the y-coordinates of A'B'C'D', we get A''=(2, 0), B''=(8, 0), C''=(2, 4), and D''=(8, 4).
3. Translation of 10 units in the negative y-direction:
To go from A''B''C''D'' to A'''B'''C'''D''', we move the points downward by 10 units, which corresponds to a translation in the negative y-direction.
Subtracting 10 units from the y-coordinates of A''B''C''D'', we obtain A'''=(2, -10), B'''=(8, -10), C'''=(2, -6), and D'''=(8, -6).
Therefore, the sequence of transformations from quadrilateral ABCD to A'B'C'D' is a reflection over the X-axis, followed by a translation of 10 units in the positive y-direction, and finally a translation of 10 units in the negative y-direction.