Which sequence of transformations will map figure K onto figure K′? Two congruent kites, figure K and figure K prime, are drawn
on a coordinate grid. Figure K has vertices at 4, 3, at 6, 5, at 4, 8, and at 2, 5. Figure K prime has vertices at 4, negative 8, at 6, negative 5, at 4, negative 3, and at 2, negative 5 Reflection across x = 4, 180° rotation about the origin, and a translation of (x + 8, y) Reflection across x = 4, 180° rotation about the origin, and a translation of (x − 8, y) Reflection across y = 4, 180° rotation about the origin, and a translation of (x + 8, y) Reflection across y = 4, 180° rotation about the origin, and a translation of (x − 8, y)
2 answers:
Answer:
The sequence of transformations will map figure K onto figure K′
is the first sequence <u>option (1)</u>
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Step-by-step explanation:
See the attached figure
as shown in the figure the K' is the image of K by reflection over x-axis
<u>But </u> We need to know which sequence of transformations will give the same result.
So, we will test the options by any point from K and its image from K'
i.e: we will test the options using the points (6,5) , (6,-5)
(6,5) ⇒ (6,-5)
<u>option (1):</u>
Reflection across x = 4, 180° rotation about the origin, and a translation of (x + 8, y)
(6,5) ⇒ (2,5) ⇒(-2,-5) ⇒ (6,-5)
<u>option (2):</u>
Reflection across x = 4, 180° rotation about the origin, and a translation of (x − 8, y)
(6,5) ⇒ (2,5) ⇒(-2,-5) ⇒ (-10,-5)
<u>option (3):</u>
Reflection across y = 4, 180° rotation about the origin, and a translation of (x + 8, y)
(6,5) ⇒ (6,3) ⇒ (-6,-3) ⇒ (2,-3)
<u>option (4):</u>
Reflection across y = 4, 180° rotation about the origin, and a translation of (x − 8, y)
(6,5) ⇒ (6,3) ⇒ (-6,-3) ⇒ (-14,-3)
As shown: The sequence of transformations will map figure K onto figure K′
is the first sequence <u>option (1)</u>
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Answer:
The length of the loop is approximately 49.58 km.
Step-by-step explanation:
Given:
Time required to ride bicycle in loop = 2 hours and 30 mins
Now we know that;
60 mins = 1 hour
30 mins =0.5 hour
so 2 hour and 30 mins =
∴ Time required to ride bicycle in loop = 2.5 hrs
Let the speed at which she is riding the bicycle be 's'.
and let Total distance of the loop be 'd'
Now we know that;
Distance is given by speed multiplied by time.
framing in equation form we get;
Now Given:
If she increase the speed by 1 km/hr, it would reduce her time around the loop by 7 minutes.
Hence we can say;
Speed =
Also time will be reduce to 7 mins.
7 mins =0.12 hrs
Now time = 2.5-0.12 =2.38
Again Distance is given by speed multiplied by time.
framing in equation form we get;
Now distance is same for both so we will calculate the speed by equating the equations.
Now Speed = 19.83 km/hr
Length of the loop (d) =
Hence the length of the loop is approximately 49.58 km.