1st Quarter Reviewer: Analytic Geometry 9 Analytic Geometry - a branch of Mathematics which deals with the properties, behaviors, and solutions of points, lines, curves, angles, and solids by means of algebraicmethods in relation to coordinate system. Two Parts of Analytic Geometry 1. Plane Analytic Geometry 2. Sold Analytic Geometry Undefined Terms in Geometry - point, line, and plane - these are the building blocks of Geometry Cartesian Coordinate System - this consists of two perpendicular lines which intersect at the point 0. - the horizontal line is called the x-axis, and the verticalline is called the y-axis. Together they are known as the Cartesian Coordinate axes. Their point of intersection 0 is called the origin. The coordinate axes divide into four quadrants marked I, II, III, IV. Distance - the length traveled at a constant speed after time - the distance between two points is the length of a straight line segment that links them - distance is always positive Formula for Distance d=(x1-x2)2+(y1-y2)2 Ex. 1. P1(-1,5) P2(5,-3) d=v(-1-5)2+(5+3)2 =V(-6)2+(8)2 = V36+ 64 = V100 = 10 units Area of a Triangle A =- bh Heron's Formula A=Vs(s-a)(s-b)(s-c) Where s= (a+b+c) Area of Triangle by Coordinates A=[x1(V2 -13) + x2(V3 - 11) + x3 (V1 - 92)] Or if made with chart A= 1 ((add the products from top left to bottom right) - (add the products from bottom left to top right)) Angle - a measure of the rotation of a line segment about a fixed point -the intersection of two lines or sides - a figure formed by two rays with the same endpoint - a geometric figure formed by two lines drawn from the same point Angle of Inclination - a straight line makes four angles with the x-axis. The smallest possible angle that the straight line makes with the positive x-axis is called its angle of inclination and its denoted by 0. - the angle is measured from the positive x-axis in a counter-clockwise direction and is never greater than 180°. - the angle between the line and the positive side of x- axis. All horizontal lines have an angle of inclination equal to 0° while all vertical lines have an angle ofinclination equal to 90°. Formula for slope - the slope denoted by the letter m, of a straight line is equal to the tangent of its angle of inclination. - m=tan a Slope of a Line - the slope, m of a line, is the tangent of the angle of inclination. - A line that rises to the right has a positive slope because the inclination is a positive acute angle; a line that rises to the left has a negative slope because. the inclination is a positive obtuse angle. The slope of a horizontal line is zero while the slope of a vertical line is undefined. Finding the angle of inclination when the slope is given - 0 = tan-1 m or 0 = arctan m Slope in terms of Coordinates -