Suppose an ant is sitting on the perimeter of the unit circle at the point (1,0). if the ant travels a distance of 2π3 in the co
unter-clockwise direction, then the coordinates of the point where the ant stops will be
2 answers:
Conclusion:
The coordinates where the ant comes to a stop are (0,1)
Detailed explanation:
We start with the ant positioned on the perimeter of the unit circle at (1,0). If it moves a distance of counterclockwise, we must determine the coordinates of where the ant halts.
The ant begins at point A.
The circumference of the unit circle is=2πr=2π(1)=2π units
The ant travels a distance of .
To find the number of complete circles made, we can divide by 2π
(This corresponds to the first circle)
(This pertains to the second circle)
After fully completing the first circle, only the first quadrant of the second circle remains.
As a result, the coordinates of the stopping point for the ant will be (0,1)
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Answer:
" Vertical angles are equal " ⇒ 2nd answer
Step-by-step explanation:
* Refer to the attached illustration
- Three lines intersect at point D.
- We have to identify the missing justification in step 3.
∵ Line FA intersects line EC at point D.
- When two lines cross, the angles created are referred to as
vertical angles.
- By the vertical angles theorem, vertical angles are equal.
Thus, ∠ADC and ∠FDE are vertical angles.
Since vertical angles are equal
∴ ∠EDF ≅ ∠ADC
Thus, m∠EDF ≅ m∠ADC
Given that m∠EDF = 120°.
∵ m∠ADC is the sum of m∠ADB and m∠BDC.
Therefore, m∠ADB + m∠BDC = 120°.
∵ m∠ADB = (3x)° ⇒ given.
∵ m∠BDC = (2x)° ⇒ given.
Thus, 3x + 2x = 120 ⇒ combine like terms.
Thus, 5x = 120 ⇒ divide both sides by 5.
Thus, x = 24.
Column (1) Column (2)
m∠EDF = 120° given
m∠ADB = 3 x given
m∠BDC = 2 x given
∠EDF and ∠ADC are vertical angles definition of vertical angles
∠EDF is equal to ∠ADC vertical angles are equal
equal
m∠ADC = m∠ADB + m∠BDC angle addition principle.
m∠EDF = m∠ADC definition of equality.
m∠EDF = m∠ADB + m∠BDC substitution.
120° = 3 x + 2 x substitution.
120 = 5 x addition.
x = 24 division.
∴ The missing justification is " vertical angles are equal "
- From the reasoning above, ∠ADC and ∠FDE are vertical angles and therefore they are equal according to the vertical angle theorem.
