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You're on a roll — 23. Transformations of a Quadrilateral First, plot the original quadrilateral ABCD. Vertices: A(-6, -1), B(-6, -4), C(3, -7), D(3, 2). Plot these points on the grid and connect them to form quadrilateral ABCD. a) Draw the image A'B'C'D' under enlargement centre (0, -1) scale factor (1)/(3). To find the image coordinates P'(x', y') of a point P(x, y) under enlargement with centre E(a, b) and scale factor k, use the formula: P'(x', y') = (a + k(x-a), b + k(y-b)) Given centre E(0, -1) and scale factor k = (1)/(3). For A(-6, -1): A' = (0 + (1)/(3)(-6-0), -1 + (1)/(3)(-1 - (-1))) A' = (0 + (1)/(3)(-6), -1 + (1)/(3)(0)) A' = (-2, -1) For B(-6, -4): B' = (0 + (1)/(3)(-6-0), -1 + (1)/(3)(-4 - (-1))) B' = (0 + (1)/(3)(-6), -1 + (1)/(3)(-3)) B' = (-2, -1 - 1) B' = (-2, -2) For C(3, -7): C' = (0 + (1)/(3)(3-0), -1 + (1)/(3)(-7 - (-1))) C' = (0 + (1)/(3)(3), -1 + (1)/(3)(-6)) C' = (1, -1 - 2) C' = (1, -3) For D(3, 2): D' = (0 + (1)/(3)(3-0), -1 + (1)/(3)(2 - (-1))) D' = (0 + (1)/(3)(3), -1 + (1)/(3)(3)) D' = (1, -1 + 1) D' = (1, 0) The coordinates of the image A'B'C'D' are: A'(-2, -1), B'(-2, -2), C'(1, -3), D'(1, 0) Plot these points and connect them to form quadrilateral A'B'C'D'. b) Draw A''B''C''D'' the image of A'B'C'D' under rotation of +ve 90° about (1, 0). To find the image coordinates P''(x'', y'') of a point P'(x', y') under a +ve 90° (counter-clockwise) rotation about a centre R(a, b), use the formula: P''(x'', y'') = (a - (y'-b), b + (x'-a)) Given centre R(1, 0). For A'(-2, -1): A'' = (1 - (-1-0), 0 + (-2-1)) A'' = (1 - (-1), 0 + (-3)) A'' = (2, -3) For B'(-2, -2): B'' = (1 - (-2-0), 0 + (-2-1)) B'' = (1 - (-2), 0 + (-3)) B'' = (3, -3) For C'(1, -3): C'' = (1 - (-3-0), 0 + (1-1)) C'' = (1 - (-3), 0 + 0) C'' = (4, 0) For D'(1, 0): D'' = (1 - (0-0), 0 + (1-1)) D'' = (1 - 0, 0 + 0) D'' = (1, 0) The coordinates of the image A''B''C''D'' are: A''(2, -3), B''(3, -3), C''(4, 0), D''(1, 0) Plot these points and connect them to form quadrilateral A''B''C''D''. c) Draw A'''B'''C'''D''' the image of A''B''C''D'' under a reflection in the line y-x = 0 (i.e., y=x). To find the image coordinates P'''(x''', y''') of a point P''(x'', y'') under reflection in the line y=x, swap the coordinates: P'''(x''', y''') = (y'', x'') For A''(2, -3): A''' = (-3, 2) For B''(3, -3): B''' = (-3, 3) For C''(4, 0): C''' = (0, 4) For D''(1, 0): D''' = (0, 1) The coordinates of the image A'''B'''C'''D''' are: A'''(-3, 2), B'''(-3, 3), C'''(0, 4), D'''(0, 1) Plot these points and connect them to form quadrilateral A'''B'''C'''D'''. d) Draw A^IVB^IVC^IVD^IV the image of A'''B'''C'''D''' under translation 2 \\ 3 and write the co-ordinate of the final image. To find the image coordinates P^IV(x^IV, y^IV) of a point P'''(x''', y''') under translation by vector a \\ b , add the translation components to the coordinates: P^IV(x^IV, y^IV) = (x''' + a, y''' + b) Given translation vector 2 \\ 3 . For A'''(-3, 2): A^IV = (-3+2, 2+3) A^IV = (-1, 5) For B'''(-3, 3): B^IV = (-3+2, 3+3) B^IV = (-1, 6) For C'''(0, 4): C^IV = (0+2, 4+3) C^IV = (2, 7) For D'''(0, 1): D^IV = (0+2, 1+3) D^IV = (2, 4) The coordinates of the final image A^IVB^IVC^IVD^IV are: A^IV(-1, 5), B^IV(-1, 6), C^IV(2, 7), D^IV(2, 4) Plot these points and connect them to form quadrilateral A^IVB^IVC^IVD^IV. Send me the next one 📸