Vocabulary and notation
What are the three undefined terms in geometry?
point, line, plane
Write the Distance Formula for two points on a number line.
AB = |a - b|
Write the Midpoint Formula for a number line.
M = (a + b) / 2
What do you call a segment, ray, line, or point that passes through a segment's midpoint?
a segment bisector
State the Segment Addition Postulate in your own words.
if B is between A and C, then AB + BC = AC
Write the correct notation for the line through points A and B
line AB (written with a double-headed arrow over AB)
Find the distance between -5 and 8 on a number line.
13
Find the midpoint of the segment with endpoints -3 and 9 on a number line.
3
True or false: three collinear points are always coplanar.
true
If AB = 9 and BC = 7, and B is between A and C, find AC.
16
Three or more points that lie on the same line are called what?
collinear
Write the Distance Formula for two points on a coordinate plane.
d = sqrt[(x2-x1)^2 + (y2-y1)^2]
Find the midpoint of the segment with endpoints (2, 4) and (8, -2).
(5, 1)
Given points at -7 and 5 on a number line, find both the distance between them and their midpoint.
distance = 12u, midpoint = -1
If AC = 20, AB = 3x + 2, and BC = 2x + 3, find x.
x = 3
Points that lie in the same plane are called what?
coplanar
Find the distance between (1, 2) and (4, 6).
5 units
A segment has midpoint M(4, 1) and one endpoint A(2, -3). Find endpoint B.
B(6, 5)
A bridge connects points A(0, 0) and B(6, 8), in kilometers. Find the length of the bridge and the location of a support pillar placed exactly halfway.
length = 10 km, pillar at (3, 4)
A hiking trail has three rest stops in a row. The distance from the first to the second is 4 km, and from the second to the third is 6 km. What is the total distance from the first to the third stop?
10 km
Can four points ever be non-coplanar? Explain using an example.
yes; any three points always determine a plane, but a fourth point is not guaranteed to lie in it
A triangle has vertices A(0, 0), B(6, 0), and C(3, 4). Find its perimeter.
AB = 6, AC = 5, BC = 5; perimeter = 16
Segment AB has endpoints A(-2, 5) and B(8, -3). M is the midpoint of AB, and N is the midpoint of AM. Find the coordinates of N.
M = (3, 1); N = (1/2, 3)
Points E(-4, 2) and F(6, -8) are the endpoints of a segment. Find its length (nearest tenth), its midpoint, and state whether the point (1, -3) lies on the segment.
length is about 14.1; midpoint is (1, -3); yes, (1, -3) lies on the segment, it is the midpoint
Points A, B, C, D lie on a line in that order. AB = x, BC = 2x + 1, CD = x + 3, and AD = 28. Find x, then find AB
x = 6; AB = 6