CC Geometry H

CC Geometry H 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.

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 picture.

. Draw a

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?

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

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

A

9) True or False?

P

B

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 point E. What is the ratio of ED : DF?

of EF from

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.

N (7,7)

M (7,6)

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