Geometry Chapter 12

Question 1

Collinear points

Answer 1

points which lie on the same straight line

Question 2

If a line passes through the points P1(x1,y1) and P2(x2,y2), then

Slope of P1P2=

Answer 2

y2-y1

x2-x1

Question 3

The distance between two points haveing the same y value is

Answer 3

the absolute value of the differences of their x values.

thus: The distance between P(6,1) and Q(9,1) is 9-6=3

Question 4

The line whose equation is y=mx+b has

Answer 4

slope m

Question 5

Using the trapezoid method can be used to find the area of a quadrilateral if

Answer 5

its verticies are given

Question 6

lines that have the same slope are

Answer 6

parallel to each other

Question 7

The locus of points such that the sum of the squares of the coordinates is a constant

Answer 7

whose center is the orgin.

The constant is the square of the radius and the equation of the circle is

x^2+y^2=r^2

Question 8

Parallel lines have

Answer 8

the same slope

Question 8

If one side of a triangle is parallel to either coordinate axis, to find the area

Answer 8

1/2bh can be used

Question 8

To find an area: If no side of a triangle is parallel to either axis then either

Answer 8

The triangle can be enclosed in a rectangle whose sides are parallel to the axes

Trapezoids whose bases are parallel to the y axis can be formed by dropping perpendiculars to the x axis

Question 9

The locus of points whose y value and x value are related by either of the equations

Answer 9

where m and b are constants, is a line

Question 10

If a line is parallel to the x-axis,

Answer 10

its inclination is 0 and its slope is 0

Question 11

The distance between the points P1(x1,y1) and P2(x2,y2) is

Answer 11

Question 12

If a line is perpendicular to the x-axis

Answer 12

its inclination is 90degrees and it has no slope

Question 14

Perpendicular lines have slopes that are

Answer 14

negative reciprocals of each other. (Negative reciprocals are numbers, such as 2/5 and -5/2 whose product is -1)

Question 15

The locus of points whose y value equals the product of a constant m and its x value is a straight line passing through the orgin;

Answer 15

its equation is y=mx

The constant m is the slope of the line

Question 16

The slope of a line equals

Answer 16

the tangent of its inclination

Question 17

The distance between two points having the same x value is

Answer 17

the absolute value of the difference of their y value.

Thus: P(2,1) and Q(2,4) is 4-1=3

Question 19

If a line slants downward from left to right

Answer 19

its inclination is an obtuse angle and its slope is negative

Question 20

The locus of points whose x value is a constant k is a line parallel to the y-axis;

Answer 20

its equation is x=k

Question 21

The locus of points whose y value is constant k is a line parallel to the x-axis;

Answer 21

its equation is y=k

Question 22

If the slope of a segment between a first point and a second equals the slope of the segment between either point and a third,

Answer 22

then the points are collinear

Question 23

If a line slants upward from left to right

Answer 23

its inclination i is an acute angle and its slope is positive

Question 24

The slope of a straight line is

Answer 24

constant all along the line