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.