Which transformation will map an isosceles trapezoid onto itself? rotation by 180° about its center, reflection across a diagona
l, reflection across a line joining the midpoints of the nonparallel sides,rotation by 360° about its center
2 answers:
Answer:
The correct option is 4.
Step-by-step explanation:
The non parallel sides of an isosceles trapezoid are congruent.
The image of an isosceles trapezoid is same as the preimage of isosceles trapezoid if
1. Reflection across a line joining the midpoints of parallel sides.
2. Rotation by 360° about its center.
3. Rotation by 360° about origin.
If we rotate the trapezoid by 180° about its center, then the parallel sides will interchanged.
If we reflect the trapezoid across a diagonal, then the resultant figure will be a parallelogram.
If we reflect across a line joining the midpoints of the nonparallel sides, then the parallel sides will interchanged.
After rotation by 360° about the center, we always get an onto figure.
Therefore option 4 is correct.
Answer: The answer is (d) rotation by 360° about its centre.
Step-by-step explanation: As shown in the attached figure, AB and CD are parallel sides of an isosceles trapezoid ABCD with centre 'O' and AD and BC are equal and non-parallel sides.
(i) If ABCD is rotated by 180° about its centre, then the new figure will not coincide with the original one. So, this option is not correct.
(ii) If ABCD is reflected across a diagonal, then also the new figure will be reverse of the original one and so this option is also incorrect.
(iii) If ABCD is reflected across a line joining the mid-points of the non-parallel sides, then also the two figures will be opposite of each other. This option will also not work.
(iv) If we rotate ABCD through 360° about centre 'O', the both the figures will coincide with each other.
Thus, the correct option is (d) rotation by 360° about its centre.
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Answer:
The expression represents the number
rewritten in a+bi form.
Step-by-step explanation:
The value of is
in term of
Substituting the value,
Product of two negative numbers is always positive.
Now in term of
Substituting the value,
Product of one negative and one positive numbers is always negative.
Now can be written as follows,
Applying radical multiplication rule,
Now, and
Now substituting the above values in given expression,
Simplifying,
Collecting similar terms,
Combining similar terms,
The above expression is in the form of a+bi which is the required expression.
Hence, option number 4 is correct.