436 FINAL QUESTIONS: ANALYTIC GEOMETRY SOLUTIONS

Make diagrams on graph paper for these questions. It really helps!

1) In what ratio does point P divide segment AB ?

a) P(2, 0), A( – 2, – 6), B(6, 6) P is the midpoint of AB, ratio is 1:1	b) P(0, 0), A(8, – 6), B(– 4, 3) ratio is 2 : 3
c) P(, 5), A(2, 7), B(–1, – 5) ratio is 5 : 6	d) P(–7, – 4), A(28, 6), B(– 14, – 6) ratio is 6 : 1

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2) The endpoints of a circle's diameter are at A(2, 3) and B(6, – 5).

a) Find the coordinates of the center of the circle. O is the midpoint of AB (4, – 1)

b) What is the measure of the radius? distance between A or B and O

3).

A(4, – 4)

B(2, 4)

C(1, 3)

D (–1, k)

Find the value of k which makes line segment AB:

a) perpendicular to line segment CD:

slope of AB = (4 + 4)/( 2 – 4) or 8/ – 2 = – 4
and because AB is perpendicular to CD, slope of CD = ¼
slope of CD = (k – 3) / ( – 1 – 1) or – ½(k – 3)
so, – ½(k – 3) = ¼ , multiply both sides by – 2 to get (k – 3) = – ½
this makes k = 5 / 2

b) parallel to line segment CD:

now, slope CD = slope AB, so – ½(k – 3) = – 4
multiply both sides by – 2, to get k – 3 = 8
k = 11

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4) While drawing the plans for a highway project, a surveyor needs to find the equation for a line that represents the path which the high-tension wires will follow. He knows that the line he needs will be parallel to the line 2x – 5y – 1500 = 0 and will include point P(500, 100).

Write the equation of this line:
a) in general form: Ax + By + C = 0

the slope must = 2/5 to be parallel to 2x – 5y – 1500 = 0, so we have a slope and a point.

2x – 5y – 500 = 0

b) in symmetric form:

set y = 0, x-intercept a = 250 ................... set x = 0, y-intercept b = – 100

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5) The diagram below depicts a map of a trapezoidal city lot. Find its area in km².

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6) A cargo boat leaves Port A (–30, – 40) heading for Port B (90, 60) but has engine trouble at P which is of the distance to B. Another boat located at C (–10, 35) must reach the cargo boat in order to make repairs on the engine. How far must the repair boat travel to meet up with the cargo boat?

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7) In the figure, triangle ABC is right-angled at B.

Prove that

8) Use h for height and b for base, then answer the step by step guide to find the Area of rectangle ABCD. Measures are in centimetres.

a) The formula for the Area of a Rectangle is: A = b× h ?

b) The measure of side DC is equal to the measure of side _AB__ ?

c) The formula for the distance between 2 points is: ?

d) The distance between A and B = ?

e) CD, the base of this rectangle measures cm.

f) ABCD is a Rectangle, so the measure of Angle DAB = _90° ?

g) This makes Line DA perpendicular_ to line AB?

h) The slope of AB = ?

i) Therefore the slope of DA = – 5 ?

j) The equation of line AD is: __y = – 5x + 12_ ?

k) The x-intercept of line AD is: __12/5 = 2.4_______ ?

l) The coordinates of D are (12/5, 0 ) = (2.4, 0)

m) The height of the rectangle =?

n) The Area of the rectangle is 40.79 × 12.23 = 499.2 cm² .

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