Which of the following is an equivalent trig ratio for sin 60.

Triangle QRS is dilated according to the rule DO,2 (x,y).

Gemiola [76]

The correct options about the dilation are; Options A, B and E

<h3>How to interpret Dilated Objects?</h3>

From the given information, find attached a dilated image.

The scale factor is 2

QRS → Q'R'S' = (x,y) → 2(x,y)

The coordinates of ∆QRS are; Q (-3, 3), R (2, 4) and S (-1, 1)

To get the coordinates of Q'R'S', we would multiply each coordinate of the original triangle by the scale factor of 2 since the dilation is from the origin. In other words, each vertex of QRS is multiplied by 2 to get each of the vertex of Q'R'S'.

2(x, y) = (2x, 2y)

The coordinates of ∆Q'R'S' becomes: Q' (-6, 6), R' (4, 8), S' (-2, 2)

To determine the statements that are true about the image ΔQ'R'S,

Starting with ΔABC, we would draw the dilation image of the triangle with a center at the origin and a scale factor of 2.

A) DO, 2 (x, y) = (2x, 2y)

A dilation about the origin with a scale factor 2 is described using the above notation.

Q' = 2(-3,3) = [2(-3), 2(3)] = (-6, 6)

R' (4, 8) = 2(2,4) = [2(2), 2(4)] = (4, 8)

S' (-2, 2) = 2(-1,1) = [2(-1), 2(1)] = (-2, 2)

Thus Option A is correct.

B) Side Q'S' lies on a line with a slope of -1

Q' (-6, 6)

S' (-2, 2)

coordinate (x, y)

Slope = m = (change in y)/(change in x)

m = (6-2)/[-6-(-2)]

m = 4/(-6+2) = 4/-4

m = -1

Option B is correct

c) QR is longer than Q'R'

Length of QR (-3 to 2) = 5

Length of Q'R' (-6 to 4) = 10

QR is not longer than Q'R'

Option C is false

d) The vertices of the image are closer to the origin than those of the pre-image.

From the diagram, the vertices of the preimage are closer to the origin than those of the dilation image.

Option D is False

e) The distance from Q' to the origin is twice the distance from Q to the origin.

The distance from Q' to the origin (6 to 0) = 6

The distance from Q to the origin (3 to 0) = 3

The distance from Q' to the origin = 2(the distance from Q to the origin)

Option E is correct.

Read more about Dilated Objects at; brainly.com/question/10253650

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8 0

2 years ago

Please Help! Will mark Brainliest for correct answer! 12 POINTS!

uranmaximum [27]

It's the second one for sure

6 0

3 years ago

Find missing angles

yKpoI14uk [10]

Hey

The value of X is 35°

X and 35° are vertically opposite angles.

Vertically opposite angles are always equal.

Hope it helps

Good luck on your assignment

8 0

3 years ago

Round your answer to the nearest hundredth.

Dmitry_Shevchenko [17]

tan 35 = BC / 2

0.700 = bc/2

bc = 1.4

3 0

2 years ago

Read 2 more answers

Julian is trying to decide on a future career. He has narrowed down his choices to orthodontist, sound engineering technician, p

Alenkasestr [34]

Percentage is the way to represent the part of a whole in a fraction of 100.The greatest percent of the increase in the number of jobs from 2006 to 2016 is orthodontist which is 10.94 percent.

<h3>Given-</h3>

In the given table we have to find out the percent of the increase in the number of each job to find out the greatest one.

<h3>Percentage</h3>

Percentage is the way to represent the part of a whole in a fraction of 100.

1-Orthodontist-

In 2006 the total number of orthodontists was 9206.

In 2016 the total number of orthodontists was 10214

Percent of increase in this job is,

$p_{1} =\dfrac{10214-9206}{9206}\times100$