To perform a 90° rotation clockwise around the origin, you take the coordinates of the point A(x, y) and transform them to A'(y, -x). Since 180° and 270° are both "steps" of 90°, we can do this in succession and achieve our goal.
1) (5, 2) 90° = (2, -5) [(y, -x)]
2) (5, 2) 180° = two 90° turns = (2, -5) rotated 90° = (-5, -2)
3) (5, 2) 270° = three 90° turns = (-5, -2) rotated 90° = (-2, 5)°
4) (-5, 2) 90° = (y, -x) = (2, 5)
5) (-5, 2) 180° = two 90° turns = (2, 5) rotated 90° = (5, -2)
6) (-5, 2) 270° = three 90° turns = (5, -2) rotated 90° = (-2, -5)
7) (-2, 5) 90° = (y, -x) = (5, 2)
8) (5, -2) 180° = (y, -x) with another 90° turn = (-2, -5) rotated 90° = (-5, 2)
solution:
Let the number be ABCDE
>>The second digit is three times the fourth digit<<
So D is 1,2, or 3 and B is 3,6 or 9.
The number is A3C1E, A6C2E, or A9C3E
>>The second digit is ... five more than the fifth digit.<<
That rules out 3 for B, so B is 6 or 9, and D is 2 or 3.
It also tells us that E is 1 or 4, so that B can be 5 more than it.
So the number is A6C21 or A9C34
>>The third digit is ... twice the fourth digit<<
So C is twice D, which is 2 or 3. So C is 4 or 6
So the number is A6421 or A9634
>>The third digit is one-half the first digit
So C is 4 because 6 is too large to be half a digit. And so
A has to be 8 so that C=4 can be half of it.
So the number is 86421.
The value of the expression 585-187 is 398
<h3>How to evaluate the expression?</h3>
The difference expression is given as:
585 - 187
The first step has already been given as:
187 - 2 = 185
For the next step, we have:
585 - ___ = 400
When the above equation is completed, we have:
585 - 185 = 400
Recall that the first step is to subtract 2 from 187.
So, the next step would be:
400 - 2 = 398
Hence, the value of the expression 585-187 is 398
Read more about difference at:
brainly.com/question/2173964
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Step-by-step explanation:
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