2008 Part B |

**Part B:**

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

5*x* – 4*y* + 48 = 0 and *y* = 0.25*x*² – 7*x* + 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 (6*x*³*y*³ – 11*x*²*y*² + 18*xy* – 5) ÷ (3*xy* – 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*) = 3*x* – 16

- What is the value of

14) The rule of function *g* is *g*(*x*) = p *x*² + r *x* – 36, where p and r are not equal to zero.

- Function

- 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. |

( *MathTub Index* )