2008 Part B

Part B:

11) A line and a parabola intersect at points A and C. Their equations are:

5x – 4y + 48 = 0 and y = 0.25x² – 7x + 41

Line segment AC is the hypotenuse of right triangle ABC, with legs // to the axes.
What are the coordinates of point B?

12) What is the result of (6x³y³ – 11x²y² + 18xy – 5) ÷ (3xy – 1)

13) In the Cartesian plane, function f is a straight line that passes through A(0, 9) and B( t, – 90).
This line is parallel to another line whose rule is g(x) = 3x – 16

What is the value of t?

14) The rule of function g is g(x) = p x² + r x – 36, where p and r are not equal to zero.

Function g is positive over the intervals .
What is the value of p?

15) Triangle PQR has these characteristics:

angle PQR = angle QRP .............. angle RPQ = 36° ............. QR = 47 cm
What is the length of segment PR to the nearest centimetre?

16) In quadrilateral ABCD, line segments TU and VW intersect at S.

Points T, U, V and W are on quadrilateral ABCD.
Quadrilaterals AVST and CWSU are congruent.
Complete steps 2 and 3 of the proof that ABCD is a parallelogram.

 Step 1 Quadrilateral AVST Quadrilateral CWSU Given Step 2 . Because . . . Step 3 AB // DC AD // BC Because . . . Step 4 ABCD is a parallelogram Because the opposite sides of a parallelogram are parallel.