Geometric transformations

I explain the basics of these congruent transformations: translation, rotation, and reflection. A rotation always happens around some point (a center point). A reflection always happens across (or in) some particular line. I also show how to use transparent paper to rotate a triangle around a point. Math Mammoth Grade 8 curriculum: Practice geometric transformations online:

I explain the basics of these congruent transformations: translation, rotation, and reflection. A rotation always happens around some point (a center point). A reflection always happens across (or in) some particular line. I also show how to use transparent paper to rotate a triangle around a point. Math Mammoth Grade 8 curriculum: Practice geometric transformations online:

We look at rotating a point 90 degrees around the origin, and how the coordinates of the point "flip" or switch, plus there is possibly a change in the sign of one of the coordinates. For example, point (5, 2) when rotated clockwise around the origin, becomes (2, -5). Then I show how to rotate a point around another point (the center point of rotation), again 90 degrees either clockwise or counterclockwise. Lastly, we rotate an entire triangle 90 degrees around a certain point in the coordinate grid. Math Mammoth Grade 8 curriculum Practice geometric transformations online:

We look at rotating a point 90 degrees around the origin, and how the coordinates of the point "flip" or switch, plus there is possibly a change in the sign of one of the coordinates. For example, point (5, 2) when rotated clockwise around the origin, becomes (2, -5). Then I show how to rotate a point around another point (the center point of rotation), again 90 degrees either clockwise or counterclockwise. Lastly, we rotate an entire triangle 90 degrees around a certain point in the coordinate grid. Math Mammoth Grade 8 curriculum Practice geometric transformations online:

We look at a few simple exercises that are based on the fact that the basic geometric transformations (translations, reflections, rotations) preserve angles, distances, and parallel lines. In other words, the image of a figure under these transformations is congruent to the original. Math Mammoth Grade 8 curriculum: Practice geometric transformations online:

We look at a few simple exercises that are based on the fact that the basic geometric transformations (translations, reflections, rotations) preserve angles, distances, and parallel lines. In other words, the image of a figure under these transformations is congruent to the original. Math Mammoth Grade 8 curriculum: Practice geometric transformations online:

In a reflection, the point and its image are at the same (perpendicular) distance from the reflection line. Learn the basics of how points are reflected in the x- or y-axis, and how their coordinates change. Math Mammoth Grade 8 curriculum: Practice geometric transformations online:

In a reflection, the point and its image are at the same (perpendicular) distance from the reflection line. Learn the basics of how points are reflected in the x- or y-axis, and how their coordinates change. Math Mammoth Grade 8 curriculum: Practice geometric transformations online:

When a figure undergoes a sequence of congruent transformations, the final figure is congruent to the original. We can use this fact to prove that one figure is congruent to another -- all we need to do is find a sequence of congruent transformations that maps one figure to the other. In this video, we look at example of such. Then I also solve an exercise where we need to find the coordinates of the vertices of a triangle before it was reflected in the x-axis and rotated 90 degrees around the origin. Math Mammoth Grade 8 curriculum: Practice geometric transformations online:

When a figure undergoes a sequence of congruent transformations, the final figure is congruent to the original. We can use this fact to prove that one figure is congruent to another -- all we need to do is find a sequence of congruent transformations that maps one figure to the other. In this video, we look at example of such. Then I also solve an exercise where we need to find the coordinates of the vertices of a triangle before it was reflected in the x-axis and rotated 90 degrees around the origin. Math Mammoth Grade 8 curriculum: Practice geometric transformations online: