Midpoint of a Line Segment class notes.notebook
March 09, 2015
Two Truths and a Lie
Have students use the write and wipe boards on top of the filing cabinet. The yellow box contains the dry erase crayons and markers. Paper towels are in the first cupboard by the desk. 1. Individually: Without discussing decide which statement you think is a
lie. Write your answer on the white board. (Have everyone hold up their
answer and look around to see if some are different.)
Minds On ...
2. Compare with your partner. Come to an agreement about which
statement is a lie. Write your answer on one white board. (Hopefully
most by now will agree on the correct answer.)
3. Compare with the whole class. (Ask students to explain why they
think each statement is true or false.)
Action ...
Consolidation ...
Lesson on Midpoint of a Line Segment
1. Let students investigate in pairs by completing the first page of the handout. Ask them to think about how the midpoint is related to the coordinates of the endpoints. For example could ask "What calculation with the original coordinates would give me the midpoint coordinates?"
2. Summarize the Midpoint Formula
3. Together complete the example on the handout page 2 and 3.
Homework: Read examples 1 and 2 on p 76 ­ 77
Review definitions on the terminology handout p 77 #1(b, d, f, h, j), 2, 4, 5, 8, 10, 11 Draw a diagram for each questions and attempt to solve using midpoint formula.
Midpoint of a Line Segment class notes.notebook
March 09, 2015
Minds On...
Two Truths and a Lie
1. Individually: Without discussing decide which statement you
think is a lie. Write your answer on the white board.
2. Compare with your partner. Come to an agreement about which
statement is a lie. Write your answer on one white board.
3. Compare with the whole class.
click to reveal statements
1. The lines y = x + 3 and y = ­x +3 are perpendicular to each other.
2. The lines 2x ­ 3y = 6 and 3x + 2y = 6 are perpendicular to each other.
3. The lines y = 4x and y = ­4x are perpendicular to each other.
1. pull for answer
2.
3.
slopes are 1 and ­1
1/1 and ­1/1 are negative reciprocals. ∴True.
rewrite the equations to
get the slopes are 2/3
and -3/2 which are neg.
reciprocals. ∴True.
slopes are 4 and -4.
They have opposite
signs, but are not
reciprocals. ∴False.
Midpoint of a Line Segment class notes.notebook
March 09, 2015
MPM 2D0 Midpoint of a Line Segment
Unit 3
1. Find the midpoint of each line segment.
a. b. N(­4, 5)
S(3, 4)
B(4, 2)
A(­2, 2) P(1, ­2) T(3, ­2)
Q(6, ­2)
M(­4, ­4)
The midpoint of AB is ( 1 , 2 )
The midpoint of PQ is ( 3.5 , ­2 )
The midpoint of ST is ( 3 , 1 )
The midpoint of MN is ( ­4 , 0.5 )
Explain how the midpoint of the horizontal and vertical segment is related to the coordinates of the endpoints.
For the horizontal lines: Average the x­coordinates and keep the y.
For the vertical lines: Average the y­coordinates and keep the x.
c.
A(1, 4)
M(3, 3)
B(5,2)
A. Form a right triangle with AB as the hypoteneuse. Call the third vertex C. (ΔABC)
B. Find the midpoint of sides AC and BC. C
C. Find the midpoint of AB.
3
The midpoint of AB is ( , )
3
.
Midpoint of a Line Segment class notes.notebook
March 09, 2015
2. Midpoint of a Line Segment Formula
Find the midpoint of a line segment AB with endpoints A(x1, y1) and B(x2, y2).
B(x2, y2)
To locate the midpoint of AB, you must "average the x­coordinates and the y­coordinates.
A(x1, y1)
Therefore, the Midpoint of a Line Segment Formula is: Example: Find the midpoint of the line segement with endpoints A(­3, 5) and B(5, 7)
3. If the midpoint of AB is M(3, 4), and the point B has coordinates B(5,6), find the coordinates of the Point A. Let point A be A(x, y)
and
.
The point is Midpoint of a Line Segment class notes.notebook
March 09, 2015
4. Verify that the diagonals of the parallelogram with vertices P(­2, 1), Q(3, 3), R(4, ­1) and S(­1, ­3) bisect each other. Recall: Diagonals are line segments connecting
non­adjacent vertices.
Q
If the diagonals bisect each other, then they divide each other into two equal parts.
P
This means they must have the same midpoints.
Calculate the midpoint of the diagonals.
R
S
PR and QS bisect each other.
Homework: Read examples 1 and 2 on p 76 ­ 77
Review definitions on the terminology handout p 77 #1(b, d, f, h, j), 2, 4, 5, 8, 10, 11
.
Draw a graph for each question #2 on and attempt to solve using midpoint formula.
Midpoint of a Line Segment class notes.notebook
March 09, 2015