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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"
Answer: The solution is (2, 2)
Step-by-step explanation:
We have the system of equations:
y = 2*x - 2
x + y = 4
The first step is to write both equations as linear equations in the slope-intercept form.
y = 2*x - 2
y = -x + 4
Now we have two lines, and we can just graph them, the easiest way is the replace the value of x and obtain two points that belong to the line, and then draw a line that passes through both lines.
For example with the first one, we can firt replace x by 0 to get:
y = 2*0 - 2
y = -2
Then the point (0, -2) belongs to this line.
Now we can replace x by 1 to get:
y = 2*1 - 2 = 0
y = 0
The point (1, 0) belongs to this line.
Then we can draw these two points in the graph, and just draw a line that passes through these two points.
Once you have your two lines drawn, the solution of the system will be the point in which the lines intersect.
Below, you can see the two lines graphed (the green is the first one and the red is the second one)
And we can see that they intersect in the point (2, 2)
Then the solution of the system is (2, 2)
