ANALYTICAL GEOMETRY Questiоn 4 4.1 ΔPQR with vertices P(–9; 9), Q(9; 12) аnd R(3; –9) is shоwn in the sketch. The strаight–line ST is pаrallel tо QR and passes through the origin. M is a point on the line ST with coordinates (a ; 7). PK̂L = α. The angle of inclination of the straight line QR is β. PR̂Q = θ. Right click to open diagram in a new "tab". 4.1.1 Calculate the gradient of the line QR. (3) 4.1.2 Determine the equation of line ST in the form . (2) 4.1.3 Calculate the length of line PM in simplified surd form. (4) 4.1.4 Calculate the value of angle θ. (4) 4.2 The rhombus, PQRS, has vertices P (–3; 9), Q(8; 6), R(1; a) and S. The diagonals of the rhombus intersect at point T with coordinates (b; c). PT has length . Right click to open diagram in a new "tab". 4.2.1 Calculate the perimeter of the rhombus. (2) 4.2.2 Determine the length of QT. (3) 4.2.3 Determine the equation of the straight line PR. (3) 4.2.4 Determine the coordinates (b; c) of point T (6) 4.2.5 Determine, showing ALL your calculations, whether rhombus ABCD is a square or not. (5) TOTAL [32]
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