Math1000 Section1.9

1. Math 1000
Stuart Jones
Section 1.9
Coordinate Geometry

2. Math 1000
Stuart Jones
In this section, we will look briefly at the midpoint and distance
formulas and then use those to work with circles.

3. Math 1000
Stuart Jones
Midpoint Formula
Theorem
For any points (x1, y1) and x2, y2), the midpoint is defined as
(
x2 + x1
2
,
y2 + y1
2
)
Find the midpoint between (-2,3) and (4,1)

4. Math 1000
Stuart Jones
Midpoint Formula
Theorem
For any points (x1, y1) and x2, y2), the midpoint is defined as
(
x2 + x1
2
,
y2 + y1
2
)
Find the midpoint between (-2,3) and (4,1)
Find the midpoint between (1,1) and (0,-7)

5. Math 1000
Stuart Jones
Distance Formula
Theorem
For any points (x1, y1) and x2, y2), the distance d is defined as
d = (x2 − x1)2 + (y2 − y1)2
Find the distance between (0,1) and (-4,5)

6. Math 1000
Stuart Jones
Distance Formula
Theorem
For any points (x1, y1) and x2, y2), the distance d is defined as
d = (x2 − x1)2 + (y2 − y1)2
Find the distance between (0,1) and (-4,5)
Find the distance between (-2,-3) and (4,-7).

7. Math 1000
Stuart Jones
We will now use these formulas to look at calculations
involving circles. Please note: ALL of the formulas must be
memorized. I cannot allow access to them on a test.

8. Math 1000
Stuart Jones
Equation of Circles
Theorem
The form of the equation of a circle in standard form is given by
(x − h)2
+ (y − k)2
= r2
, where (h, k) is the center and r is the radius.

9. Math 1000
Stuart Jones
Equation of Circles
Theorem
The form of the equation of a circle in standard form is given by
(x − h)2
+ (y − k)2
= r2
, where (h, k) is the center and r is the radius.
Find the equation of a circle centered at (3, 2) with a
radius of 2.

10. Math 1000
Stuart Jones
Equation of Circles
Theorem
The form of the equation of a circle in standard form is given by
(x − h)2
+ (y − k)2
= r2
, where (h, k) is the center and r is the radius.
Find the equation of a circle centered at (3, 2) with a
radius of 2.
Find the equation of the circle whose diameter’s endpoints
are given by (−1, 4) and (0, 5).

11. Math 1000
Stuart Jones
More Circle Questions.

12. Math 1000
Stuart Jones
More Circle Questions.
Find the equation of a circle whose diameter’s endpoints
are given by (1, 3) and (5, 3).

13. Math 1000
Stuart Jones
More Circle Questions.
Find the equation of a circle whose diameter’s endpoints
are given by (1, 3) and (5, 3).
Find the equation of a circle whose center is (3, 5) and
passes through (5, 5)

14. Math 1000
Stuart Jones
The Bottom Line
The Midpoint and Distance formulas (given above) are
very important in calculations involving circles.
This section has quite a few formulas. Make sure to spend
some time making sure you know the formulas and how to
use them.