April 03, 2017
Aim #8: How do find midpoints of segments and points that divide
segments into 3, 4, or more proportional, equal parts?
CC Geometry R
Do Now:
a) Plot the points A(-4,5) and B(12,13) and draw AB.
b) Determine the midpoint of segment AB.
How did you find it?
c) Can you find it using another method?
Midpoint Formula:
The midpoint of the segment with endpoints (x1,y1) and (x2,y2) is
Examples:
1) Find the midpoint of the segment
with endpoints (-8, 7) and (-2, -3).
3) If the midpoint of segment AB is M(1,-2)
and A is (6,1), find the coordinates of B.
( , )
.
2) Find the midpoint of the segment with
endpoints (-7, 4) and (2, 5).
4) If the midpoint of segment CD is
M(23,-6) and C is (-4,11),
find the coordinates of D.
April 03, 2017
5) 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?
6) What are the coordinates of the point on the directed line segment from A(-4,5) to B(12,13)
that partitions the segment in the ratio 2:3?
7) Point P is on segment AB such that AP : PB is 4:5. If A has coordinates (4,2) and B has
coordinates (22,65) determine and state the coordinates of P?
April 03, 2017
7) The endpoints of DEF are D(16, 8) and F(1, -2). Determine and state the
coordinates of point E, if DE : EF = 2:3.
8) 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. What is the
location of the robot at the end of the third hour?
b. 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?
April 03, 2017
Name ______________________
Date ______________________
CC Geometry R
Hwk. #8
1. Find the midpoint of (-5, 3) and (-1, -7).
2. The endpoints of the diameter of a circle are (-6, 4) and (8, 2). Find the
coordinates of the center of the circle.
3. The midpoint of LN is the point M(-2, 2). If the coordinates of N is (2, 8),
find the coordinates of point L.
4. What are the coordinates of the point on the directed line segment from A(-7,-2)
to B(14,12) that partitions the segment in the ratio 4:3?
5. What are the coordinates of the point on the directed line segment from
A(2,-3) to B(5,13) that partitions the segment in the ratio 3:1?
April 03, 2017
6. Find the point on the directed segment from (-3,-2) to (4,8) that divides it into
a ratio of 3:2.
7. 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). If the robot does not change speed or direction, where will it be 3
hours into its journey?
8. The center of a circle has the coordinates (-1, 5).
If the coordinates of one endpoint of the diameter is (-4, 3),
a) find the coordinates of the other endpoint.
b) Find the length of the diameter in simplest radical form.
9. As shown on the set of axes below, ∆GHS has vertices G(3,1), H(5,3) and
S(1,4). Graph and state the coordinates of ∆G”H”S”, the image of ∆GHS after
the transformation T-3,1(D2(∆GHS)).
April 03, 2017
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