Deck 11: Analytic Geometry

Question 1

Find the slope m and value of b at the y -intercept (0, b )for the graph of the equation .

Answer 1

NOT ANSWERED.

Question 2

If and the slope of line is , then the slope of is .

Answer 2

True

Question 3

Find the slope of any line that is perpendicular to the line .

A)
B)
C)
D)

Answer 3

D

Question 4

The drawing shown can be used to prove that the line segment joining the midpoints of two sides of a triangle is parallel to the third side.

Question 5

The line with equation y = mx + b has slope m and contains the point (0, b).

Question 6

Find the area of , which has vertices at A (-2,-3), B (-2,4)and C (5,4).

A)
B)
C)
D)

Question 7

Using rectangle HJKL as shown, what type of quadrilateral is determined by joining the midpoints of the sides of HJKL in order?

Question 8

The graph of the line contains the points (6, 0)and (0, 4).

Question 9

For the isosceles triangle shown, the coordinates of the vertex have not been provided.In order, use a, b, c, etc as needed to name the coordinates of the vertex.

Question 10

What type of quadrilateral is shown? Be as specific as possible.

A)parallelogram
B)trapezoid
C)isosceles trapezoid
D)kite

Question 11

The fourth vertex of the parallelogram shown is ( ).

Question 12

What is the slope of the line shown?

A)
B)
C)
D)

Question 13

Find the slope of a line that is perpendicular to the line through the points ( a , b )
and ( ).

Question 14

Find the Slope-Intercept form of the equation whose graph has slope m = 2 and the y-intercept at (0,-3).

A)
B)
C)
D)

Question 15

Which equation must hold true if the parallelogram shown is a rhombus?

A)
B)
C)
D)None of These

Question 16

The line shown has a positive slope.

Question 17

What is the slope of any line that is perpendicular to the graph of ?

Question 18

For to be an isosceles triangle with , state an equation that relates s , t , and v .

Question 19

Where ,find the slope m of the line that contains the points ( a ,3)and ( b ,3).

Question 20

Where , the slope of the line through the points ( )and ( )is .

Question 21

Find the distance between the points (-4,3)and (5,3).

Question 22

Find the slope m of the line that contains the points (-3,-4)and (1,4).

Question 23

If midpoints are involved in a proof, then a general point should be represented by ( ).

Question 24

Find the point of intersection for the lines whose equations are and .

A)
B)
C)
D)

Question 25

Where , the distance between the points ( a , c )and ( b , c )is ( )units.

Question 26

Find the midpoint of the line segment that joins (2a,0)and (0,2b).

Question 27

What type of quadrilateral has vertices with coordinates (0,0), (a,0), (a,b), and (0,b)? Be asspecific as possible.

A)parallelogram
B)square
C)rhombus
D)rectangle

Question 28

If points A and B have symmetry with respect to the origin, find B if A = ( ).

Question 29

To show analytically that two lines are parallel, one applies the Slope Formula.

Question 30

Find the area of the triangle with vertices at (2a,0), (2c,0), and (0,2b).

Question 31

Find the slope of any line that is parallel to the line that is the graph of the
equation .

Question 32

Find the distance between the points (3,-4)and (-2,8).

A)5
B)12
C)13
D)None of These

Question 33

The intersection of the lines x = a and y = b is the point (b, a).

Question 34

Where A = (4,-7)and M = (3,-2), point M is the midpoint of . Find the coordinates for
point B .

Question 35

For the isosceles triangle shown, which of the following must be true?

A)The three medians are congruent.
B)The medians to the congruent sides are equal in length.
C)The medians to the congruent sides are perpendicular.
D)None of These

Question 36

In the form , find the equation of the line that contains ( g , h )and is perpendicular to .

A)
B)
C)
D)None of These

Question 37

According to the Midpoint Formula, the midpoint of the line segment that joins
( )and ( )is .

Question 38

Find the distance between the points (-7,-5)and (5,4).

Question 39

(not shown)has vertices A (0,0), B (2 a ,2 b ), and C (0,2 c ). Where M is the midpoint
of and N is the midpoint of , how are the lengths of and related?

Question 40

Given that A = (-3,-7)and B = (5,2), find the midpoint of .

Question 41

For the parallelogram ABCD with vertices A (0, 0), B ( a , 0), C ( ), and D ( b , c )to be
a rhombus, it is necessary that .

Question 42

The midpoint of the hypotenuse of a right triangle is equidistant from the threevertices of the triangle.

Question 43

Find the midpoint of the line segment that joins (-1,4)and (7,-8).

A)(6,-4)
B)(-3,-2)
C)(3,-2)
D)None of These

Question 44

Find the area of , which has vertices at (0,0), (8,0), and (5,6).

Question 45

What is the value of x at the point of intersection of the lines and ?

Question 46

The line that contains ( )and (6, b )has slope .
Find the value of b .

Question 47

Find the y-coordinate of point X = (4,?), a point that lies on the graph of the equation .

Question 48

What type of triangle has vertices at (-a,0), (a,0), and (0,b)?

A)right
B)obtuse
C)equilateral
D)isosceles

Question 49

Which formula would be applied to prove the theorem, "The diagonals of a rectangle are congruent.?"

Question 50

According to the Distance Formula, the distance between the points
( )and ( )is .

Question 51

For square ABCD, two of the vertices are A = (0,0)and B = (a,0). Provide coordinatesfor the remaining vertices.

Question 52

Let the vertices of be the points M (0,0), N ( a ,0), P ( ), and Q ( b , c ). Which equation must hold true if the diagonals of are perpendicular?

A)
B)
C)
D)

Question 53

The graphs of the equations and are the same line.

Question 54

Lying on the x-axis are 2 points whose distance from (2,-3)is 5 units. Find the x-coordinatesof these points (a,0)that lie on the x-axis.

Question 55

If the diagonals of a parallelogram are congruent, then the parallelogram isa rhombus.

Question 56

Determine the value of x so that the points (-2,4), (1,1), and (x,6)are collinear.

Question 57

In the form , find the equation of the line through (-2,-5)and (1,4).

Question 58

The triangle with vertices at (0, 0), (0, b), and (a, 0)is a right triangle with the vertex of the rightangle at the point (0, 0).

Question 59

Points A and B have symmetry with respect to the x-axis. If A = (4.5,-6.3), findthe coordinates of point B.

A)(4.5,6.3)
B)(-4.5,6.3)
C)(-4.5,6.3)
D)None of These

Question 60

Find the value of b so that the points (-1,3), (1,-1), and (3,b)are collinear.

Question 61

The midpoint of the line segment that joins the point (0,0,0)to the point (2,-2,2)is the point (1,-1,1).

Question 62

Where a, b, c, d, . . . , and n are real numbers, explain why the line
        
has the direction vector

.

Question 63

Determine the exact volume of the sphere .

A)192
B)96
C)76
D)46

Question 64

Show that for any value of , the point having the form

 lies on the
plane whose equation is

.

Question 65

Which line is parallel to the graph of ?

A)
B)
C)
D)

Question 66

In the form , find the equation of the line through (0,-3)and (2,1).

Question 67

In the form , find the equation of the line that is the perpendicular- bisector of the line segment that joins (0,0)and (2 a ,2 b ).

A)
B)
C)
D)

Question 68

For the equation , find in the form an equivalent equation
in which the coefficient (multiplier)of x is the number -9.

Question 69

Find the point of intersection for the lines that are the graphs of and .

Question 70

Explain why the plane  is a plane of symmetry for the sphere 

.

Question 71

In the form , find the equation of the line that contains (5,2)and has the
slope of .

Question 72

The point lies in the plane .

Question 73

For any point  in Cartesian space, explain why the point  is the
point of symmetry with respect to the origin.

Question 74

Find the point that is the y -intercept of the line .

A)(4, 0)
B)(0, 3)
C)(0, -3)
D)None of These

Question 75

In Cartesian space, the point (0,6,0)lies 6 units above the origin.

Question 76

The line through the points ( a , 3)and (4, -1)is perpendicular to the line . Determine the value of a .

A)-4
B)4
C)12
D)-12

Question 77

The lines which are the graphs of and intersect at one point.

Question 78

In Cartesian space, the direction of the line is represented by the vector or any nonzero multiple of this vector.

Question 79

Explain why the lines decribed below are parallel.
         and

Question 80

Find the general form for the line through the points (-2,3)and (4,-1).

A)
B)
C)
D)None of These