Objectives: 1. To do all kinds of things with points in the Cartesian plane: distance, midpoint, slope, equation 2. To solve an equation for a particular variable Assignment: Ignore the book instructions. Find the distance, midpoint, slope and equation in point-slope form for these three problems: • P. 10: 35, 38, 39 • Homework Supplement • Read: P. 14-21; P. 30 Rectangular Coordinates Cartesian Plane Origin Quadrants Ordered Pair Pythagorean Theorem Midpoint Slope Linear Equation How can you locate this point quantitatively? Can you do it in more than one way? The Cartesian Coordinate Plane is a flat place where points hang out • Usually called a “graph” • Uses ordered pairs of real numbers to locate points • Gives a visual representation of the relationship between x and y (Also called a Rectangular Coordinate System) 1596-1650 French philosopher-etc. Cogito Ergo Sum A fly taught him about the Cartesian coordinate plane and analytic geometry, for which he took full credit Find each of the following using the two points on the graph: 1) The distance between the points 2) The midpoint between the points 3) The slope of the line between the two points 4) The equation of the line between the points You will be able to find the distance between two points In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. c2 a2 b2 Graph 𝐴𝐵 with A(2, 1) and B(7, 8). Add segments to your drawing to create right triangle ABC. Now use the Pythagorean Theorem to find AB. If the coordinates of points A and B are (x1, y1) and (x2, y2), then AB x2 x1 2 y2 y12 To the nearest hundredth of a unit, what is the approximate length of 𝑅𝑆, with endpoints R(3, 1) and S(−1, −5)? The distance between (−4, k) and (4,4) is 10 units. Find the value of k. You will be able to find the midpoint between two points If A(x1,y1) and B(x2,y2) are points in a coordinate plane, then the midpoint M of 𝐴𝐵 has coordinates x1 x2 y1 y2 , 2 2 Find the midpoint of the segment with 3 endpoints at (−1, 5) and 2, 3 . The midpoint C of 𝐼𝑁 has coordinates (4, −3). Find the coordinates of point I if point N is at (10, 2). Slope can be used to represent an average rate of change. • A rate of change is how much one quantity changes (on average) relative to another. • For slope, we measure how y changes relative to x. The slope m of a nonvertical line is the ratio of vertical change (the rise) to the horizontal change (the run). Find the slope of the line passing through the 4 5 3 points −5, −2 and 10, −2 . Find the value of k such that the line passing through the points (−4, 2k) and (k, −5) has slope −1. You will be able to write the linear equation between two points Censored A linear function can have many forms, pick your favorite: • Slope-Intercept Form: y mx b • Point-Slope Form: y y1 m x x1 • Standard Form: Ax By C Write the equation of the line through the points (−2, 5) and (4, −7). Write your answer in point-slope, slope-intercept, and standard forms. You will be able to solve an equation for any variable Page 7 of your book contains these helpful formulas. Number them thusly: 1. 2. 3. 4. 5. 6. 7. 8. 9. Given any of the previous formulas, what would it mean to solve for a particular variable? To solve for a variable in an equation or formula means to isolate that variable on only one side of the equation: variable = everything else Solve 𝑉 = 𝜋𝑟 3 for r. 4 3 Objectives: 1. To do all kinds of things with points in the Cartesian plane: distance, midpoint, slope, equation 2. To solve an equation for a particular variable Assignment: Ignore the book instructions. Find the distance, midpoint, slope and equation in point-slope form for these three problems: • P. 10: 35, 38, 39 • Homework Supplement • Read: P. 14-21; P. 30

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