Now let’s plot the points on the coordinate grid and label the vertices. The rule for 90° counterclockwise rotation is \((x,y)\) becomes \((-y,x)\), let’s apply the rule to find the vertices of our new pentagon. Let’s start by finding the coordinates of the vertices of our original pentagon. Rotate pentagon QRSTU 90° counterclockwise to create pentagon Q’R’S’T’U’. Pentagon QRSTU is shown on the coordinate grid. Therefore, kite KLMN was rotated 180° about the origin to create kite K’L’M’N’. Let’s look at the rules, the only rule where the values of the x and y don’t switch but their sign changes is the 180° rotation. Let’s start by identifying the coordinates of the vertices of kite KLMN and of our rotated kite:Ī closer look at the coordinates of the vertices shows that the coordinates of K’L’M’N’ are the same as the vertices of the original kite but with the opposite sign. Can you identify which rotation of kite KLMN created kite K’L’M’N’? The kite has been rotated about the origin to create the kite K’L’M’N’. Kite KLMN is shown on the coordinate grid. Now I want you to try some practice problems on your own. Let’s apply the rules to the vertices to create quadrilateral A’B’C’D’: To rotate quadrilateral ABCD 90° counterclockwise about the origin we will use the rule \((x,y)\) becomes \((-y,x)\). Let’s apply the rule to the vertices to create the new triangle A’B’C’: Let’s rotate triangle ABC 180° about the origin counterclockwise, although, rotating a figure 180° clockwise and counterclockwise uses the same rule, which is \((x,y)\) becomes \((-x,-y)\), where the coordinates of the vertices of the rotated triangle are the coordinates of the original triangle with the opposite sign. To rotate triangle ABC about the origin 90° clockwise we would follow the rule (x,y) → (y,-x), where the y-value of the original point becomes the new \(x\)-value and the \(x\)-value of the original point becomes the new \(y\)-value with the opposite sign. Now that we know how to rotate a point, let’s look at rotating a figure on the coordinate grid. 270° counterclockwise rotation: \((x,y)\) becomes \((y,-x)\)Īs you can see, our two experiments follow these rules.
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