Geometry Module 1 OMS

Midpoint Formula

100

Find the midpoint between the two points.                (-8, 4) (2, 9)

(-3, 6.5)

200

Find the midpoint. (-6, -2) (4, 0) 

(-1, -1)

300

Find the midpoint between A and B is A is located at -20 and B is located at 12.

-4

400

Find the endpoint if B is the midpoint. A(5, 2) B(6, 4) C(?,?)

C(7, 6)

500

Find the endpoint if B is the midpoint. A(-1, -2) B(11, -4) C(?,?)

C(23, -6)

Weighted Averages

100

A is located at -4 with a weight of 6 and B is located at 2 with a weight of 3. 

-2

200

B is located at -6 and weighs three times as much as D. D is located at 2. 

-4

300

X weighs four times as much as Z, and Y weighs three times as much as X. X is located at -4, Y is located at 0, and Z is located at 5. 

-11/8 or -1.375

400

U weighs twice as much as X. U(-8, -5) X(2, 0)

(-14/3, -10/3)

500

A handyman services customers from two towns that are 50 miles apart. He wants to install an office between the two cities using weighted averages based on calls received from each city. If one city has a weight of 3, and the other 5, how far from the first city should he place his office? 

31.25 miles

Vocabulary

100

A location in space

point

200

Something that is proven true

Theorem

300

How do you name a plane?

With 3 non-collinear points

400

How do you name a line?

With two collinear points. 

500

What does collinear mean?

Same line. 

SAP

100

XY = 12, YZ = 2x, XZ = 28. Y is between X and Z. Find the length of YZ.

5

200

XY = 11d, YZ = 9d - 2, XZ = 5d + 28. Y is between X and Z. Find the length of YZ.

16

300

XY = 7a, YZ = 5a, XZ = 6a + 24. Y is between X and Z. Find the length of YZ.

20

400

A carpenter has a piece of wood that is 78 inches long. He wants to cut it so that one piece is five times as long as the other piece. What are the lengths of the two pieces?

13 in & 65 in

500

A straight railroad track is being built to connect two cities. The measured distance of the track between the two cities is 160.5 miles. A mail stop that is between the two cities and lies along the track is 28.5 miles from the first city. How far is the mail stop from the second city?

132 mi

Partitioning a line

100

Find P on AF such that the ratio of AP to PF is 1:3. A is located at -15 and F is located at 1.

-11

200

Find B on AC such that the ratio of AB to BC is 3:4. A is located at -5 and C is located at 7.

1/7

300

Find X on AE such that AX to XE is 1:2. A is located at -8 and E is located at 7.

-3

400

Find C on AB such that AC to CB is 1:2. A(-5, -2) B(6, 2)

C(-4/3, -2/3)

500

Find R on QS such that QR to RS is 2:3. Q(-2, -1) S(8, 5)

R(2, 1.4)