The quadrant numbers of a coordinate plane increase in the counterclockwise direction; you must measure angle in a coordinate plane the same way to be consistent.
A positive angle is measured counterclockwise; a negative angle is measured clockwise.
When asked to plot the image of point A under a dilation about point B with a scale factor, it means stretch it/scaling it up or down around the point B. (About the origin would mean (0,0))
Think of scale factor as multiplication (eg. Scale factor of 3 means that the distance between point A & point B will be 3 times further under the dilation in the same direction)
Reflections across the x-axis or y-axis involve finding the opposite of a number. Rotations by multiples of 90 degrees about the origin also involve number opposites.
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You can use the Pythagorean theorem to find the distance between two points on a coordinate plane.
To find the point where the right angle is created, take the x value of one point and the y value of the other point (eg. Point 1 (-5,8) and point 2 (4,6) create (-5,6). Then look at the difference to find the leg lengths.
When you translate something in geometry, you don't distort it in any way.
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Properties of translations
Property 1: Line segments are taken to line segments of the same length.Property 2: Angles are taken to angles of the same measure.Property 3: Lines are taken to lines, and parallel lines are taken to parallel lines.
There are two properties of every rotation: the center and the angle.
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Determining the center of rotation
Rotations preserve distance, so the center of rotation must be equidistant from a point and its image. If you take the segments that connected each point of the image to the corresponding point in the pre-image, the center of rotation is at the intersection of the perpendicular bisectors of all those segments.
The image under dilation will be the scale factor times as far from the center of dilation in the same direction compared to the pre-image.
Eg. The pre-image has a distance of 5 from the center while the image as a distance of 10 when the scale factor is 2.
Remember to dilate image's distance from the center of dilation as well as its size.
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The line of reflection should contain the midpoint between corresponding points of the image and pre-image.
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