My answer is D. Is that right? If not, what is the right answer and how did you get it?
Use a rotation matrix to rotate figure DEFGH clockwise 90º. If the figure has coordinates D (1, 3), E (3, 2), F (1, -1), G (-3, -2), and H (-2, 2), which statement is true about figure D'E'F'G'H'?
A) E' = (2, -3)
B) G' = (2, 2)
C) F' = (1, 1)
D) H' = (-2, 3)
+130511 I don't think your answer is correct....rotating (-2,2) 90 degrees clockwise puts us in the 1st quadrant. And since H is already in the 2nd quadrant at (-2, 2), it can't remain in the 2nd quadrant at (-2,3). The likely candidate for the correct answer is A. Follow the logic...If E is in the 1st quadrant, its x and y coordinates are positive. Then, rotating it 90 degrees clockwise would put it in the 4th quadrant....Hence, the x coordinate would be positive and the y coordinate would be negative.... the rotational matrix for this is given by
| cos90 sin90 |
| -sin90 cos 90 |
So we have
| cos90 sin90 | x l 3 l
| -sin90 cos 90 | l 2 l ..... and this gives.......
(3 cos 90 + 2 sin 90) = ( 0 + 2) = 2 ......for the resulting x coordinate
And ( -3sin 90 + 2cos 90)= (-3 + 0 ) = -3 .......for the resulting y coordinate
Yup...just as I suspected !!!.....the resulting point is (2. -3) and "A" is the correct choice.....
+130511 I don't think your answer is correct....rotating (-2,2) 90 degrees clockwise puts us in the 1st quadrant. And since H is already in the 2nd quadrant at (-2, 2), it can't remain in the 2nd quadrant at (-2,3). The likely candidate for the correct answer is A. Follow the logic...If E is in the 1st quadrant, its x and y coordinates are positive. Then, rotating it 90 degrees clockwise would put it in the 4th quadrant....Hence, the x coordinate would be positive and the y coordinate would be negative.... the rotational matrix for this is given by
| cos90 sin90 |
| -sin90 cos 90 |
So we have
| cos90 sin90 | x l 3 l
| -sin90 cos 90 | l 2 l ..... and this gives.......
(3 cos 90 + 2 sin 90) = ( 0 + 2) = 2 ......for the resulting x coordinate
And ( -3sin 90 + 2cos 90)= (-3 + 0 ) = -3 .......for the resulting y coordinate
Yup...just as I suspected !!!.....the resulting point is (2. -3) and "A" is the correct choice.....
