Mathematics 3206
Name:______________________
Investigation #4 – The Midpoint of a Line Segment
(p 162)
Section 4.2
An architectural and construction firm called Buildings For Us has been contracted to help build three new
chalets for a resort. Three chalets already exist on the property.
The blueprint of the resort’s property shows the property on a grid, with the main building located at P (0, 0).
The three existing chalets are located at A (1, 3), B (11, 7), and C (8, 3). The blueprint scale is 1 unit = 10 m.
The resort owner has requested that each new chalet be 0placed exactly halfway between two of the existing
chalets. At what coordinates should Buildings For Us build the new chalets?
Purpose
Find the coordinates of the midpoint of a segment.
Procedure
•
Plot and label the positions of the existing chalets (namely A(1, 3), B(11, 7), and C(8, 3)) on the
coordinate grid below. Join the points to form
∆ABC
.
y
x
•
Find the midpoint of each side of the triangle.
•
Fill in the table below to show the coordinates where the three chalets should be built?
Placement of New Chalets
Between Chalet A and Chalet B
Between Chalet B and Chalet C
Between Chalet A and Chalet C
Coordinates of New Chalets
Questions
1. What general method can be used to determine the coordinates of the midpoint of a line
segment?
2. Find the midpoints of the sides of
Side
_____
DE
_____
DF
_____
EF
∆DEF
if the vertices are D(-1, 3), E(2, 5) and F(12, 7).
Workings to determine midpoint
Midpoint