Aim #11: How do we divide segments into proportional, equal parts (day 2)?Do Now: 1) What are the coordinates of the point on the directed line segment from D(-5,-1) to E(7,2) that partitions the segment in the ratio 2:1? Use of the grid is optional.

CC Geometry H

2) Find the midpoint of: a) (-8, 7) and (-2, -3) b) (-7, 4) and (2, 5)

3) If the midpoint of segment AB is M(1,-2) and A is (6,1) find the coordinates of point B.

4) Given points P(10,10) and Q(0,4), find point R on PQ such that . Draw a picture.

5) A robot is at position A(40,50) and is heading toward the point B(2000,2000) along a straight line at a constant speed. The robot will reach point B in 10 hours.

a. What is the location of the robot at the end of the third hour?

b. What is the location of the robot 5 minutes before it reaches point B?

c. If the robot keeps moving along the straight path at the same constant speed as it passes through point B, what will be its location at the twelfth hour?

6) Given points A(3,-5) and B(19,-1), find the coordinates of point C that sits of the way along AB, closer to A than to B.

7) Point C lies of the way along AB, closer to B than to A. If the coordinates of point A are (12,5) and the coordinates of point C are (9.5, -2.5), what are the coordinates of point B?

b) Find the length of AB in simplest radical form.

8) a. If the midpoint of segment AB is M(-1, 5) and A is (-4,3) find the coordinates of point B.

9) True or False?

a. AP : PB = 3:2 b. AP : AB = 2:5 c. PB : AB = 2:5

d. BP : PA = 2:3 e. AB : AP = 5:3

10) Given a line segment from E to F. Point D lies on the segment of EF from point E. What is the ratio of ED : DF?

11) Point P partitions directed segment AB in the ratio of 3:4. If A(-9,-9) and B(5,-2), find the coordinates of point P.

12) Given a directed segment from M to N as shown below. Find the coordinates of partition point P that divides the segment into a 5:2 ratio.

A P B

M

N

(7,6)

(7,7)

13) Dan has buried his treasure in a shallow lake. He drew a map, shown below, to help remember the exact location. Follow the 3 steps to find the coordinates of the treasure.

1st- P1 partitions the directed segment from (1,3) to (10,9) in a ratio of 1:2. Label P1.

2nd- P2 partitions the directed segment from (3,8) to (8,2) in a ratio of 4:1. Label P2.

3rd- The treasure will be located at the midpoint of the segment connecting P1 and P2. At what point is the treasure buried?

14) a. Below, directed segment AB is divided by construction into 5 equal segments. Which of the points divides AB in the ratio of 2 to 3? _____

15) Determine the ratio of the directed segment AB (initial point A) when partitioned by point P.

a) b)

c) d)

A BR S T U

b. Directed segment BA is divided by construction into 5 equal segments. Which of the points divides BA in the ratio of 2 to 3? _____

A

P

BP

A

B

B

PA

B P

A

Name: ______________________ CC Geometry HDate: ____________ HW #11

1) Find the midpoint of ST given S(-2,8) and T(10,-4).

2) Find the point on the directed line segment from (-2,0) to (5,8) that divides it in the ratio 1:3.

3) Given points A(3,-5) and B(19,-1), find the coordinates of point C such that .

4) a. Given F(0,2) and G(2,6). If point S lies of the way along FG, closer to F than to G, find the coordinates of S.

b. What is the slope of FG?

c. What is the slope of FS?

d. What is the slope of SG?

e. Why do FS and FG have to have the same slope as FG?

5) A robot begins its journey at the origin, point O, and travels along a straight line path at a constant rate. Fifteen minutes into its journey the robot is at A(35,80).

a. If the robot does not change speed or direction, where will it be 3 hours into its journey (call this point B)?

b. The robot continues past point B for a certain period of time until it has traveled an additional the distance it traveled in the first 3 hours and stops.

i. How long did the robot‛s entire journey take?

ii. What is the robot‛s final location?

iii. What was the distance the robot traveled in the last leg of its journey, to the nearest tenth?

Mixed Review:1) In right triangle ABC with the right angle at C, sin A = 2x + 0.9 and cos B = 6x − 0.7. Determine and state the value of x. Explain your answer.

2) Using a compass and straightedge, construct an altitude of triangle ABC below. [Leave all construction marks]

A

B C

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