On each of the given triangles, perform a rotation of 180∘ about point X. Shade the quadrilateral formed and give the most specific name for the quadrilateral in the spaces below.

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diascordicm5 · Accepted Answer

Step 1  Let (a,b) be a point  If (a,b) and point X lies on same horizontal axis then on rotating (a,b) 180∘ its coordinate changes to (-a,b)  If (a,b) and point X lies on same vertical axis then on rotating (a,b) 180∘ its coordinate changes to (a,-b)  If (a,b) and point X does not lies on same axis then on rotating (a, b)180∘ its coordinate changes to (-a,--b)  After rotation if opposite sides are equal then figure formed is a parallelogram  After rotation if opposite sides are equal and both diagonals are also equal then figure formed is a rectangle  After rotation if all sides are equal then figure formed is a rhombus  Step 2    Let coordinate of X be (0,0)  Then vertices of triangle is    After rotation coordinate changes to  (3, 0)→(−3, 0)  (−3, 0)→(3, 0)  (−1, −2)→(1, 2)  Quadrilateral is    From above figure, opposite sides are equal   Thus, quadrilateral formed is parallelogram  Step 3    Let coordinate of X be (0,0)  Then vertices of triangle is    After rotation coordinate changes to  (0, 2)→(0, −2)  (0, −2)→(0, 2)  (−2, 0)→(2, 0)  Quadrilateral is    From above figure, all sides are equal   Thus, quadrilateral formed is rhombus  Step 4    Let coordinate of X be (0,0)  Then vertices of triangle is    After rotation coordinate changes to  (3, 0)→(−3, 0)  (0, 1)→(0, −1)  (0, −1)→(0, 1)  Quadrilateral is    From above figure, all sides are equal   Thus, quadrilateral formed is rhombus

On each of the given triangles, perform a rotation of

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