Math 1321 – Exam I – September 20, 2001 Name ___________________________________
1. Let A(a, b) and B(c, d) be endpoints of some segment AB. Use the coordinates of AB – a,b,c,d to write down the formula
a) to find the midpoint of AB
b) to find the point P(x,y) that is 4/5ths of the way from A to B.
c) to find the undirected distance from A to B
d) slope of the line segment AB
2. Write down these other formulas
a) the quadratic formula used to solve equations of the form
ax2 + bx + c = 0
x =
b) the angle of intersection  of two lines with slope m1 and m2 respectively. Describe m2.
tan  =
c) distance from the line ax + by + c = 0 to the point P( r, q) ( HINT: use coordinates of P )
3. Fill in the blank
A _________________________ is a relation in which no ordered point of the relation has the same
first coordinate but different second coordinate.
If  represents the angle of inclination of a given of a line then the _____________ of the line is
defined as tan  .
A function f is said to be _____________ provided f( -  ) = f(  )
A function f is said to be ___________________ on some interval I provided f(x1) < f(x2) for
every x1 < x2 in the interval I.
4.
Draw a rectangular coordinate system
a) label the axes, the quadrants and
b) plot the points A ( - 4, 6 ) and B ( 0, - 2 )
5. Find the length of the hypotenuse of a right triangle that has vertices
A(1, 1), B(4, -1), and C(3, 4)  _____________________ Find its area = ___________
6. Determine whether the following three points line are on the same line or not
A( 2, - 2 ), B ( - 1, - 6 ) and C ( 4, 4 ). Show Work
7. Complete the following right triangle.
8. A point on the x-axis is known to be equidistant from A(3, -1) and B( -5, 7) .
Find the point - both coordinates !
9. Which one he following terms best satisfies the statement “ a parallelogram with adjacent sides
perpendicular “
parallelogram,
rectangle,
quadrilateral
triangle,
rhombus,
10. Find each of the following absolute values. Simplify by using the idea of absolute values.
Exact values - no calculators.
a) | 5 - \/ 17 | = ________
b) | 8 - 3 | = ________
square
11.
line with slope m = \/ 3
intersects a vertical line at what acute angle ? ________________
12. What is the angle of inclination of a line with m = - 1 ? _________________
13. Draw a triangle with sides ABC, where A is the vertex at the origin, mAB = 1/2, mBC = -4, and
mAC = - 2
Find the measure of the largest angle.
14. Identify as just RELATIONS or more specific - FUNCTIONS .
a) y = | x |
b) x2 + y2 = 16
c) y = x2 + 2x - 1
14.5 Draw each of the following
a) x = - 2
b) y = 2x + 4
15.
Identify each of the following lines as ; vertical, horizontal, slant, or not a line
_________________ a . y = - 4
__________________b. x = 3y
_________________ c. x2 = 1 – y
15.5 Identify each of the following as a circle , a point, no graph, or a line
_______________ a. ( x+ 2)2 - 16 = - ( y + 2 )2
_______________ b. ( x – 3 )2 + ( y – 2)2 = 0
16. What is the center and the radius of a circle with a diameter AB, where A(2, - 3) and B( -2, 0 )
17. Give a description of the graph of ( x + 2)2 + ( y – 4 )2 = 4
17.5 Find the equation of the circle with center at ( 2, 0 ) and radius \/ 5
18. Use determinants to find one of the following two problems ( Clearly tell which one your are
doing - cross out the other one )-- Show work on the back of previous page
a) find the equation of the line that passes through the points ( 2, -3 ) and ( 4, 1 ) or
b)
Find the area of the triangle with vertices A(2,1), B(3, 2) and C( - 2, 0 )
19. Find the slope of the line that
a) is parallel to the x-axis and passes through the point ( -2, 2 ). _________________________
b) is perpendicular to y = 3x – 2 and passes through ( 0, 2 ). __________________________
20. Find the equation of the line that
a) passes through ( 2, 0) and ( 0, 4). ___________________
b) is parallel to x + 2y = 1 and goes through the origin. ____________
c) is a member of the family y – 2 = m( x + 3 ) and has an undefined slope. ______________
21. Identify as even, odd, or neither
a) f(x) = 2x
b) f(x) = 4x + 2
22. Prove that if c > 0 and
f(x) = cx + 2 , then f(x) is increasing.
23. Prove the following statement by using an analytic proof --Do not use proofs from geometry.
Prove the diagonals of a rhombus are perpendicular.
25. A backpacker looks through a ground telescope at a height of 5 feet and sees the reflection of a
mountain top in a pool of water 440 feet in front of him. The mountain is known to be 10560 feet
away from the pool. How high is the mountain ?
26. A person 6 feet tall is standing near a street light so that he s 4/10 of the distance from the pole to the
tip of his shadow. How high above the ground is the lightbulb ? If the person’s head is exactly 5
feet from the lightbulb, how far is the person from the pole ?
28.
What is the distance between the lines 3x + 4y = 12 and 3x + 4y = 24 ?