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A is the point (-6,7),B is the point (-2,7) and C is the point (1,1). (a) Quadrilateral ABCD has rotational symmetry about the midpoint of AC. Find the coordinates of D. (b) Find the equation of (i) AB, (ii) AD. (c) Find the coordinates of the point where AD cuts the x-axis.

1313. A A is the point (−6,7),B (-6,7), B is the point (−2,7) (-2,7) and C C is the point (1,1) (1,1) .\newline(a) Quadrilateral ABCD A B C D has rotational symmetry about the midpoint of AC A C . Find the coordinates of D D .\newline(b) Find the equation of\newline(i) AB A B ,\newline(ii) AD A D .\newline(c) Find the coordinates of the point where AD A D cuts the (−6,7),B (-6,7), B 11-axis.

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Q. 1313. A A is the point (−6,7),B (-6,7), B is the point (−2,7) (-2,7) and C C is the point (1,1) (1,1) .\newline(a) Quadrilateral ABCD A B C D has rotational symmetry about the midpoint of AC A C . Find the coordinates of D D .\newline(b) Find the equation of\newline(i) AB A B ,\newline(ii) AD A D .\newline(c) Find the coordinates of the point where AD A D cuts the (−6,7),B (-6,7), B 11-axis.
  1. Calculate Midpoint of AC: Calculate the midpoint of AC.\newlineMidpoint formula: ((x1+x2)/2,(y1+y2)/2)((x_1 + x_2)/2, (y_1 + y_2)/2).\newlineMidpoint of AC = ((−6+1)/2,(7+1)/2)=(−5/2,8/2)=(−2.5,4)((-6 + 1)/2, (7 + 1)/2) = (-5/2, 8/2) = (-2.5, 4).
  2. Find Coordinates of D: Find the coordinates of D using rotational symmetry about the midpoint of AC.\newlinePoint B is 4.54.5 units to the right and 33 units up from the midpoint.\newlineSo, D will be 4.54.5 units to the left and 33 units down from the midpoint.\newlineCoordinates of D = (−2.5−4.5,4−3)=(−7,1)(-2.5 - 4.5, 4 - 3) = (-7, 1).
  3. Equation of AB: Find the equation of AB.\newlineBoth AA and BB have the same yy-coordinate, so ABAB is a horizontal line.\newlineEquation of a horizontal line: y=ky = k, where kk is the yy-coordinate.\newlineEquation of ABAB: y=7y = 7.
  4. Equation of AD: Find the equation of AD.\newlineSlope formula: (y2−y1)/(x2−x1)(y_2 - y_1) / (x_2 - x_1).\newlineSlope of AD = (1−7)/(1−(−6))=−6/7(1 - 7) / (1 - (-6)) = -6 / 7.\newlinePoint-slope form: y−y1=m(x−x1)y - y_1 = m(x - x_1).\newlineEquation of AD: y−7=(−6/7)(x+6)y - 7 = (-6/7)(x + 6).

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