Math Reviewer PDF 10-AOM

MATH REVIEWER From 10-AOM (chan :>) Pointers covered: 1.​ Distance and Midpoint Formula 2.​ Equation of a Circle I.​ Distance and Midpoint Formula Distance Formula The distance between two points (𝑥1, 𝑦1)(𝑥1, 𝑦1) and...

MATH REVIEWER From 10-AOM (chan :>) Pointers covered: 1.​ Distance and Midpoint Formula 2.​ Equation of a Circle I.​ Distance and Midpoint Formula Distance Formula The distance between two points (𝑥1, 𝑦1)(𝑥1, 𝑦1) and (𝑥2, 𝑦2)(𝑥2, 𝑦2) in a Cartesian plane is given by the formula:(𝑥1, 𝑦1)(𝑥1, 𝑦1) 𝑎𝑛𝑑 (𝑥2, 𝑦2)(𝑥2, 𝑦2) 2 2 𝐷= (𝑥2 − 𝑥1) + (𝑦2 − 𝑦1) This formula is derived from the Pythagorean Theorem and is useful for determining the straight-line distance between two points. Midpoint Formula The midpoint of a line segment connecting two points (𝑥1, 𝑦1)(𝑥1, 𝑦1) and (𝑥2, 𝑦2)(𝑥2, 𝑦2) is calculated using the formula: 𝑥1 + 𝑥2 𝑦1 + 𝑦2 𝑀= ( 2 , 2 ,) This formula helps to determine the center point between two given points. II.​ Equation of a Circle The general equation of a circle with center (h,k)(h, k) and radius rr is given by: 2 2 2 (𝑥 − ℎ) + (𝑦 − 𝑘) = 𝑟 Where: ​ h,k = coordinates of the center of the circle ​ r = radius of the circle Circumference is the distance around a circle  𝐶 = 2π𝑟 Area is the region occupied by the circle 2 𝐴 = π𝑟 Standard Form of the Equation of a Circle If the equation of a circle is given in the general quadratic form: 2 2 2 (𝑥 − ℎ) + (𝑦 − 𝑘) = 𝑟