Task 3: A sequence of transformations was applied to triangle ABC to result in A"B"C". First, ABC was rotated 90 counterclockwise around the
origin to get A'B'C'. Then a translation resulted in A"B"C".
1. What are the coordinates of A'B'C' after the rotation?
(Hint: you need to do the rotation)
A’ ( , )
B'( , )
C'( , )

2. What is the algebraic description of the translation in
this sequence? (Hint: A'B'C' is the preimage: A”B”C” is the image.)
(x, y) → (X —————, y ————-)
(Include both the sign and the number)

step-by-step explanation:

1

the value of x is 9 ⇒ answer b

step-by-step explanation:

* we can solve this problem using cosine and sine rule

- in δ abc

∵ ab = 36 , bc = 28 , ac = 16

- lets find the measure of angle b using the cosine rule

∵ cos b = [ab² + bc² - ac²]/2(ab)(bc)

∴ cos b = [36² + 28² - 16²]/2(36)(28)

∴ cos b = 19/21

∴ m∠b = cos^-1(19/21) ≅ 25°

- lets find the measure of angle a using the sine rule

∵ sina/bc = sinb/ac = sinc/ab

∴ sina/28 = sin25°/16 ⇒ by using cross multiplication

∴ sina = 28 × sin25°/16

∴ sina = 0.7396

∴ m∠a = sin^-1(0.7396) ≅ 48°

- from the figure m∠abd = m∠dbc

∵ m∠abc = 25°

∴ m∠abd = 25°/2 = 12.5°

- in δabd

∵ m∠a = 48° , m∠abd = 12.5°

∵ the sum of the measures of the interior angles of any δ is 180°

∴ m∠adb = 180° - (48° + 12.5°) = 119.5°

∵ ab = 36

∵ ad = x

- use the sine rule to find x

∵ sin∠adb/ab = sin∠abd/x

∴ sin119.5°/36 = sin12.5°/x ⇒ by using cross multiplication

∴ x = 36 × sin12.5°/sin119.5° = 8.95 ≅ 9

* the value of x is 9

the answer is c. ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

step-by-step explanation: