What is the formula to find the volume of the solid ?
1 answer:
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Answer:
The sequence is as following:
1. Reflection 180°
2. Reflection over the line x=5
3. Translation 2 units down.
Step-by-step explanation:
The question is as following:
Describe the sequence of transformations from Quadrilateral WXYZ to W”X”Y”Z”.
The picture is a coordinate plane with
W= (-8,8)
X= (-2,8)
Y= (-2,4)
Z= (-8,4)
W”= (2,-10)
X”= (8,-10)
Y”= (8,-6)
Z”= (2,-6)
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See the attached figure
The sequence is:
Reflection 180° ⇒ Reflection over the line x=5 ⇒ translation 2 units down.
Rule of reflection 180° is (x, y) → (–x, –y)
Rule of reflection over the line x=5 is (x, y) → (–x+10 , y)
Rule of translation 2 units down is (x, y) → (x , y–2)
The way of thinking:
1. The rectangle at the second quadrant, we need make it at the fourth quadrant, so, the suitable is <u>Reflection 180°</u>
2. After reflection 180°, it is noticed that we need reverse the vertices so we need to make a reflection over its vertical axis which is at <u>x = 5</u>
3. We need to translate it 2 units down to overlap with the required coordinates.
<u>Check the points:</u>
W(-8,8) ⇒ (8,-8) ⇒ (2,-8) ⇒ (2,-10)⇒W"
X(-2,8) ⇒ (2,-8) ⇒ (8,-8) ⇒ (8,-10)⇒X"
Y(-2,4) ⇒ (2,-4) ⇒ (8,-4) ⇒ (8,-6)⇒Y"
Z(-8,4) ⇒ (8,-4) ⇒ (2,-4) ⇒ (2,-6)⇒Z"
Options:
(2, 2), (3, 1), (4, 2)
(2, 2), (3, –1), (4, 1)
(2, 2), (1, –2), (0, 2)
(2, 2), (1, 2), (2, 0)
Answer:
A. (2, 2), (3, 1), (4, 2)
Step-by-step explanation:
Given
Required
Solve for x and y
To solve this, we make use of graphical method (see attachment for graph)
All points that lie on the shaded region are true for the inequality
Next, we plot each of the given options on the graph
A. (2, 2), (3, 1), (4, 2)
All 3 points lie on the shaded region.
<em>Hence, (a) is true</em>
