Use the slider to rotate AABC about point P through different angles of rotation (a). As you move the slider, you'll see the ima
ge, AA'B'C'.
move on the screen. At what angles of rotation does AA'B'C' coincide with each of the other triangle images?
move on the screen. At what angles of rotation does AA'B'C' coincide with each of the other triangle images?
1 answer:
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Answer:
1. (x - 3)² = 8
2. (x + 2)² = 3
3. (x + 6)² =
4. (x + 3)² = 27
5. (x + 4)² = 13
6.
Step-by-step explanation:
Completion of Square:
In the following problems the terms in the RHS of the above equation may be missing. We balance the equation. Simplify it and re write it in terms of LHS.
1. x² - 6x + 1 = 0
Taking the constant term to the other side, we get:
x² - 6x = - 1
⇒ x² - 2(3)x = -1
⇒ x² -2(3)x + 9 = - 1 + 9 [Adding 9 to both the sides]
⇒ x² -2(3)x + 3² = 8
⇒ (x - 3)² = 8 is the answer.
2. 3x² + 12x + 3 = 0
Note that the co-effecient of x² is not 1. We make it 1, by dividing the whole equation by 3. And then proceed like the previous problem.
3x² + 12x = -3
Dividing by 3 through out, x² + 4x = - 1
⇒ x² + 2(2) + 4 = -1 + 4
⇒ x² +2(2) + 2² = 3
⇒ (x + 2)² = 3 is the answer.
3. 2x² + 24x = 29
x² + 12x =
⇒ x² + 2(6)x + 36 = + 36
⇒ x² + 2(6)x + 6² =
⇒ (x + 6)² = is the answer.
4. x² + 6x - 18 = 0
x² + 6x = 18
⇒ x² + 2(3)x = 18
⇒ x² + 2(3)x + 9 = 18 + 9
⇒ x² + 2(3)x + 3² = 27
⇒ (x + 3)² = 27 is the answer.
5. x² + 8x + 3 = 0
x² + 8x = -3
⇒ x² + 2(4)x = -3
⇒ x² + 2(4)x + 16 = - 3 + 16
⇒ x² + 2(4)x + 16 = 13
⇒ (x + 4)² = 13 is the answer.
6. 9x² - 30x + 6 = 0
9x² - 30x = - 6
⇒ x² x = - 6
is the answer.