Applications of Math 10
Midpoint Formula
MIDPOINT
o the point that is an equal distance between two other points.
o because it is a point it is written as any other point on the grid would be written (x, y)
o the following formula will calculate the midpoint between two points.
Given the points
Ax1 , y1  and Bx2 , y2  then the Midpoint of AB is:
 x1  x2 y1  y2 
,


2 
 2
Midpoint Formula
Examples:
1) Given the two points, find the midpoint of A and B.
a)
A(6, 9) and B(-2, -7
c)
E(12, 6) and F(-10, 9)
b)
C(2, -8) and D(-5, 9)
d)
G(-2, 3) and H(5, 6)
2) A line segment UP has a midpoint of M(5, 5). Suppose the coordinates of one endpoint, U, are
(2, 10). What are the coordinates of the other endpoint, P?
3) The vertices of a rhombus are B(1, 4), L(8, 8), U(7, 0), and E(0, -4).
a)
Sketch the rhombus on a coordinate grid.
b)
Determine the midpoint of the diagonal BU.
8
6
4
c)
2
Determine the midpoint of the diagonal LE.
-8
-6
-4
-2
2
4
6
-2
-4
d)
-6
What do you notice about the
midpoints of the diagonals?
-8
_________________________________________
-10
e)
Determine the slope of BU.
f)
Determine the slope of LE.
g)
What do the slopes tell you about the diagonals of a rhombus?
Midpoint Assignment.
Complete each questions showing all the proper steps.
1. State the coordinates of the midpoint of each line segment below.
F
8
C
Midpoint of CD________________
6
4
Midpoint of EF________________
2
D
-8
-6
-4
-2
2
4
6
8
10
-2
H
-4
E
Midpoint of GH________________
-6
-8
-10
G
8
10
Applications of Math 10
Midpoint Formula
2. Determine the coordinates of the midpoint of the line segment for each pair of endpoints given
below.
a) (1, 1) and (7, 9)
a____________
e) (6, -5) and (1, -7)
e____________
b) (5, 3) and (-3, 0)
b____________
f) (-6, 5) and (3, -2)
f____________
c) (-9, -2) and (5, -4)
c____________
g) (1.6, 2.7) and (4.6, 3.3)
g____________
d) (4, -3) and (-7, -3)
d____________
h) (-2.9, 10.2) and (1.4, 21.4) h____________
3. On a map with numerical coordinates in kilometres, the town of Baxter is at (5.4, 6.3) and the town
of Trent is at (12.2, 1.5). The road joining Baxter and Trent is a straight line. A service station is to be
built on this road so that it is the same distance from both towns. Determine the coordinates of the
position of this new service station.
4. A radar centre gives the location of a vessel as a pair of coordinates. The coordinates represent the
ship’s distance east and north of the radar centre, measured in kilometres. A cruise ship has a location of
(240, 160). A ferry is located at the position (120, 310). A fishing boat is halfway between these two.
Determine the coordinates of the location of the fishing boat.
5. The graph below shows a profile of a hike. What are the coordinates of the midpoints between each section
of the height?
5. A line segment OK has endpoints at O(1, 7) and K(25, 15).
a) Determine the midpoint of OK and label it point M.
b) Determine the coordinates of two other points that, along with M, will divide OK into four
equal parts.
12
8
4
4
8
12
16
20
24
7. The endpoints of a diameter of a circle are C(5, 5) and D(-1, -3).
a) What are the coordinates of the centre of the circle?
b) Use the distance formula to find the radius of the circle.
c) Use the distance formula to determine if the point (-2, 4) lies on the circle.
8. Determine the midpoints of the segments joining the following pairs of points: Use the midpoint formula.
a)
P1(2, -5) and P2(4, 1)
d)
P1(4, 0) and P2(3, 7)
b)
P1(0, -2) and P2(6, 4)
e)
P1(-6, -10) and P2(2, -4)
c)
P1(5, -8) and P2(-3, 2)
f)
P1(6.8, 1.2) and P2(5.4, 2.7)