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katrin2010 [14]
2 years ago
13

6. Triangle ABC is rotated 90 degrees counterclockwise and then translated 3 units up to form

Mathematics
1 answer:
joja [24]2 years ago
7 0

Given:

Consider triangle ABC is rotated 90 degrees counterclockwise and then translated 3 units up to form triangle A'B'C'.

To find:

The transformation that can be used to map each point (x,y) on Triangle ABC to its corresponding point on Triangle A'B'C'.

Solution:

If a figure rotated 90 degrees counterclockwise, then

(x,y)\to (-y,x)

P(x,y)\to P_1(-y,x)

If a figure translated 3 units up, then

(x,y)\to (x,y+3)

P_1(-y,x)\to P'(-y,x+3)

If  triangle ABC is rotated 90 degrees counterclockwise and then translated 3 units up to form triangle A'B'C', then the rule of transformation is

(x,y)\to (-y,x+3)

Therefore, the required rule of transformation is (x,y)\to (-y,x+3).

Note: Option are not in proper form.

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Please solve with explanation (high points)
Hunter-Best [27]

Step-by-step explanation:

so, we have a large triangle made of the 2 cables as legs and the ground distance AB as baseline.

the tower is the height to the baseline of that large triangle.

let's call the top of the tower T.

and remember, the sum of all angles in a triangle is always 180°.

we know the angle A = 62°, and angle B = 72°.

assuming that AB is a truly horizontal line that means that the 2 legs (cables) have different lengths, the triangle is not isoceles, and the tower is not in the middle of the baseline.

so, the height (tower) splits the baseline into 2 parts. let's call them p and q.

p + q = 12 m

p = 12 - q

let's simply define that p is the part of the baseline on the A side, and q is the part of the baseline on the B side.

we have now 2 small right-angled triangles the large height (tower) splits the large triangle into.

one has the sides

AT, height (tower), p

angle A = 62°

angle T = 180 - 90 - 62 = 28°

the other has the sides

BT, height (tower), q

angle B = 72°

angle T = 180 - 90 - 72 = 18°

now remember the law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

with the sides and the associated angles being opposite.

p/sin(28) = height/sin(62)

q/sin(18) = height/sin(72)

we know from above that

p = 12 - q

so,

(12 - q)/sin(28) = height/sin(62)

height = (12 - q)×sin(62)/sin(28)

q/sin(18) = height/sin(72)

height = q×sin(72)/sin(18)

and therefore, as height = height we get

(12 - q)×sin(62)/sin(28) = q×sin(72)/sin(18)

(12 - q)×sin(62)×sin(18) = q×sin(72)×sin(28)

12×sin(62)×sin(18) - q×sin(62)×sin(18) =

= q×sin(72)×sin(28)

12×sin(62)×sin(18) = q×sin(72)×sin(28) + q×sin(62)×sin(18) =

= q×(sin(72)×sin(28) + sin(62)×sin(18))

q = 12×sin(62)×sin(18) / (sin(72)×sin(28) + sin(62)×sin(18))

q = 4.551603755... m

p = 12 - q = 7.448396245... m

height = q×sin(72)/sin(18) = 14.00839594... m ≈ 14 m

the cell tower is about 14 m tall.

7 0
1 year ago
I have NO idea how to do this to be honest.
vazorg [7]
(-5a)(-3a ²)
= 
15a³

-5 x -3 = 15 ( negative times negative = positive)
a x a² = a³ ( when multiplying exponents, you add the exponents together )
4 0
2 years ago
Read 2 more answers
Question 3 of 10
Aleks [24]
C=+3 since your adding three more onto four
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3 years ago
OMG PLEASE HELP! THIS ASSIFNMENT DUE IN LIKE 5 MINUTES!! (Sorry if blurry pic)
Ber [7]

Answer:

I think the 3rd answer

Step-by-step explanation:

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2 years ago
Does this mean they are calling me on insta?
patriot [66]

Answer:

yessss this mean they are calling you

have a great day

<h2> BRINDLIST plz </h2>

<u>Mrslenbox</u>

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2 years ago
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