In the diagram below, ∆ PQS is drawn with vertices P (-2 ; 3), Q (3 ; 6) and S in a Cartesian plane. Line QS passes through the origin at O. PS║QR.

PŜQ 20,23^{0}.

3.1 Calculate the gradient of QS. (2)

3.2 Calculate the size of 𝜃. (2)

3.3 Determine the:

3.3.1 gradient of PS, round off to the nearest number. (4)

3.3.2 equation of PS (3)

3.4 If it is further given that the equation of QS is y = 2𝑥, determine the coordinates of S. (4)

3.5 Calculate the length of QS, in simplified surd form. (3)

3.6 Calculate the area of ∆PQS, rounded off to two decimal digits. (5)

3.7 If it is further given that PQRS is a parallelogram, determine the coordinates of R. (3)

3.8 A(5 ; 4), B(0 ; -1) and C(t ; 2) are collinear points, determine the value of t. (4)

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