given right triangle ABC with altitude BD drawn to hypotenuse AC. If BD = 24 nd DC = 12, what is the length of AD?
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"
