![]() ![]() We have to think through plus and minus signs for the new coordinates based on the quadrants. So the new x value has the same absolute value as the old y value, and vice versa. So the horizontal and vertical switch places in a 90 degree rotation. When we rotate it 90 degrees, anything horizontal becomes vertical, and anything vertical becomes horizontal. So we see a triangle, the purple triangle has a horizontal leg, a long horizontal leg, and a short vertical leg. For a 90 degree rotation either way, the x-distances, and y-distances swap place. Recall the discussion about perpendicular slopes a few lessons ago. So we swap back and forth between I and III, or swap back and forth between II and IV. Any point that rotates in 180 degrees will move to the opposite quadrant. So I, II, III, IV back to I, that's the counterclockwise direction of rotation. So, if it's in I, it's gonna get moved to II, from II to III, from III to IV, and from IV back to I. Any point that rotates 90 degrees counterclockwise will go up a quadrant. ![]() If it's in quadrant IV, it would go to III, from III it will go to II, from II it will get to I, from I it will go to IV, that's the clockwise direction, IV to III to II to I, back to IV. Any point that rotates 90 degrees clockwise will go down a quadrant. In these cases, the center of rotation will almost always be the origin, and the angle will either be 90 degrees, one way or the other, or 180 degrees. Sometimes the test also asks about rotations in the x-y plane. ![]() In the previous video, I talked about reflections in the x-y plane. ![]()
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