^The amount we subtract is the length of the new line AD. ^Observe that the X coordinate of A, ^line OB, is greater than the ^ x-coordinate of P prime, line OC. ^Similarly, drop a perpendicular ^from P prime to get point C. ^Now, let's reverse the rotation, ^and drop a perpendicular from A, ^to the x-axis to define a point B. ![]() ![]() So, we drop a perpendicular from P prime to the x-axis to define a new point A. This looks like the situation we saw in the previous video when we rotated the point one zero on the x-axis. First, let's rotate the diagram, and imagine OP is the X-axis. We need to construct some other points to help us, so let's go back to what we already know, and break down the problem. (wind whistling) (gun cocking) Let's call the point we start with, p, and the point it gets rotated to, p prime. ![]() And it'll take us a little work to get there, so roll up your sleeves and tie back your hair. (light turns on) ^(xylophone sound) A more elementary way to derive these formulas is using the basic definitions of Trigonometry. One is to use properties of linear transformations. So knowing x, y, and theta, you can compute x prime and y prime, but where do these formulas come from? Well there's a couple of different ways to get these formulas. Y prime equals x sine theta plus y cosine theta. X prime equals x cosine theta minus y sine theta. The formulas we'll come up with aren't too complicated, in fact, here they are. That is if we start with an arbitrary point, x y, we'd like to know the coordinates of x prime y prime, with a point where it ends up after rotation. To create our software tools for setting up shots, we need to have formulas for where every point goes when rotated. When plot these points on the graph paper, we will get the figure of the image (rotated figure).(bouncing noises) - Now we know the coordinates of a few ^special points when they're rotated. In the above problem, vertices of the image areħ. When we apply the formula, we will get the following vertices of the image (rotated figure).Ħ. When we rotate the given figure about 90° clock wise, we have to apply the formulaĥ. ![]() When we plot these points on a graph paper, we will get the figure of the pre-image (original figure).Ĥ. In the above problem, the vertices of the pre-image areģ. First we have to plot the vertices of the pre-image.Ģ. So the rule that we have to apply here is (x, y) -> (y, -x).īased on the rule given in step 1, we have to find the vertices of the reflected triangle A'B'C'.Ī'(1, 2), B(4, -2) and C'(2, -4) How to sketch the rotated figure?ġ. Here triangle is rotated about 90 ° clock wise. If this triangle is rotated about 90 ° clockwise, what will be the new vertices A', B' and C'?įirst we have to know the correct rule that we have to apply in this problem. Let A(-2, 1), B (2, 4) and C (4, 2) be the three vertices of a triangle. Let us consider the following example to have better understanding of reflection. Here the rule we have applied is (x, y) -> (y, -x). Once students understand the rules which they have to apply for rotation transformation, they can easily make rotation transformation of a figure.įor example, if we are going to make rotation transformation of the point (5, 3) about 90 ° (clock wise rotation), after transformation, the point would be (3, -5).
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