Given:
The right angle triangle with legs 4 units and 7 units.
To find:
The length of hypotenuse.
Solution:
Pythagoras theorem: In a right angle triangle,
Let x be the length of the hypotenuse.
Using the Pythagoras theorem for the given triangle, we get
Taking square root on both sides, we get
[∵Side length cannot be negative]
Therefore, the length of the missing side for the given right angle triangle is 8.06 units.
Answer:
i) A. 180º rotation about the origin, ii) .
Step-by-step explanation:
i) In this case, we understand that vertex changed to
after doing an operation. At first we must calculate the distance of each point regarding origin by Pythagorean Theorem:
Point P:
If we know that ,
,
and
, the distance
is:
Point P':
If we know that ,
,
and
, the distance
is:
As , origin is the center of rotation.
Besides, is a multiple of
, that is:
1) Given
2)
3) Scalar multiplication of a vector/Result.
The value of the scalar proves that P experimented a 180º rotation about the origin. Hence, the correct answer is A.
ii) If and the same operation described in item i) is used, then, the location of
is:
Which corresponds to option C.