Solutions 2008 Part B |

**Solutions 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?

**Solution:** We need the *x* value at A and the *y* value at C for the coordinates of B.

- First, find the points of intersection of the 2 curves: (I use ¼ instead of 0.25)

- From 5

- Multiply through by 4 and collect terms to get:

- This factors as: (

- To find the

12) What is the result of (6*x*³*y*³ – 11*x*²*y*² + 18*xy* – 5) ÷ (3*xy* – 1)

**Soln:**

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

**Soln:** since the lines are parallel, their slopes must be equal.

- Therefore so

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?

**Soln:** We have a parabola opening upwards with **zeros at – 6 and 10**,

- so we substitute

- 0 = p ( – 6)² + r ( – 6) – 36 , and 0 = p ( 10)² + r (10) – 36

- We turn these into:

- Now we add them together to eliminate "r":

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?

**Soln:** We have an isosceles triangle with equal sides PQ and PR.

- We know the vertex angle is 36° so the 2 other angles are each = ½(180° – 36°) = 72°.

- When we draw the perpendicular PS from P to QR, we know that S is the mid-point.

Since QR = 47 cm (given), SR = 23.5 cm.

- In triangle PSR, we know that = 76 cm.

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 corresponding angles in congruent figures are congruent. |

Step 3 | AB // DC AD // BC |
Because alternate angles are equal, so lines are parallel. |

Step 4 | ABCD is a parallelogram | Because the opposite sides of a parallelogram are parallel. |

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