436 FINAL QUESTIONS: ANALYTIC GEOMETRY

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)	b) P(0, 0), A(8, – 6), B(– 4, 3)
c) P(, 5), A(2, 7), B(–1, – 5)	d) P(–7, – 4), A(28, 6), B(– 14, – 6)

.

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.

b) What is the measure of the radius?

.

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
b) parallel to line segment CD

.

4) While drawing the plans for a highway project, a surveyor needs to find the equation for a line that represents the path 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,
b) in symmetric form.

5) The diagram below depicts a map of a trapezoidal city lot. Find its area in km ².

.

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?

.

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) The measure of side DC is equal to the measure of side _____ ?

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

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 = ____ ° ?

g) This makes Line DA _____________ to line AB?

h) The slope of AB = _________ ?

i) Therefore the slope of DA = ______ ?

j) The equation of line AD is: _________________ ?

k) The x-intercept of line AD is: _________ ?

l) The coordinates of D are (__ , ___ ).

m) The height of the rectangle = ______________ ?

n) The Area of the rectangle is __________ .

.

( Analytic Geometry MathRoom Index )

.

(all content of the MathRoom Lessons © Tammy the Tutor; 2004 - ).