Circles and coordinates
Any spelling of the right answer counts: 0.5 or 1/2, pi/2 or π/2, sine or cosine for the same graph.
Your score, on every device
Free account: your score and streak follow you to any device, and you can practice from a photo of your worksheet.
Try a sample flashcard set- Read-only with Canvas
- Free to start
- Never does your work
- Made by a student
About Circles and coordinates
A slice of a circle is a fraction of the whole: an arc is that fraction of the circumference and a sector is that fraction of the area, with the fraction set by the central angle out of 360°. An inscribed angle, whose corner sits on the circle, is always half the arc it opens onto.
On the coordinate plane, the distance formula is Pythagoras in disguise, the midpoint is the average of the two points, and a circle is every point at distance r from its center, which is exactly what (x − h)² + (y − k)² = r² says.
Keep in mind
- Arc length = (angle/360) × 2πr. Sector area = (angle/360) × πr².
- A central angle equals its arc. An inscribed angle is half its arc.
- An angle inscribed in a semicircle is 90°.
- Distance = √((x₂ − x₁)² + (y₂ − y₁)²). Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2).
- Circle: (x − h)² + (y − k)² = r², center (h, k), radius r. Complete the square to get there from x² + y² + Dx + Ey + F = 0.
The Backpack iPhone app is coming soon to the App Store