Geometry Chapter 13 Review

The distance d between points and is: Example 2 Find the distance between (–3, 4) and (1, –4). Why? Let’s try an example to find out! (-3, 4).. (1, -4) 4 8 Pythagorean Theorem! 4√5

An equation of the circle with center (a, b) and radius r is: Let’s analyze (x – 0) 2 + (y – 0) 2 = 81 to see if it really is a circle!! How could this be a circle?

Find the center and radius of each circle. Sketch the graph Center: (2, -4) Radius = 3.

Example 1b: Find the slope of the line. -5 – (-2) = 3 – (- 1) x y.. (-1, -2) (3, -5) y 2 – y 1 = x 2 – x 1 slope - 3 = 4 The slope of the line is __

Positive Slope Greater than 1 Uphill Steep Positive Slope Less than 1 Uphill Flatter Negative Slope Greater than 1 Downhill Steep Negative Slope Less than 1 Downhill Flatter Slope = 0 Undefined Slope Running up the hill is undefined!

A line with slope 4/3 passes through points (4, -5) and (-2, __ ). Use the slope formula to find the missing y coordinate. 4 3 = y – (-5) -2 – = y Simplify and solve as a proportion -24 = 3y = 3y y = y

Parallel lines have slopes that are equal. Perpendicular lines have slopes that are opposite inverses(change the sign and flip).

The Midpoint Formula The midpoint of the segment that joins points (x 1,y 1 ) and (x 2,y 2 ) is the point (-4,2) (6,8) (1,5)

Exercises 3. M (3,5) A (0,1) B (x,y) (6,9) This is the midpoint To find the coordinates of B : x-coordinate: 3 = 0 + x 2 6 = 0 + x x = 6 y-coordinate: 5 = 1 + y 2 10 = 1 + y y = 9

II. Standard Form: (Ax + By = C). Getting x and y intercepts: (x, 0) and (0, y) 1) 2x + 3y = Try the cover up method!!!. (0, 2). (3, 0) yx

II. Slope-Intercept Form (y = mx + b): m = slope; b = y-intercept y = 2. (0, 4)..... yorizontal Why? Thus y=2!!. (-1, 2). (6, 2). (-6, 2)

III. Finding Slope-Intercept Form: (y = mx + b) 3x – 4y = 10 m = _____ b = _____ -3x -4y = -3x y = 3/4x – 5/2 3/4 -5/2

IV. Systems of Equations: Two lines in a coordinate plane can do two things: (1) intersect (perpendicular or not) (2) not intersect (parallel) SystemsAlgebraicGraph By Substitution 2x + y = 8 y = 2x Isolate a variable first. This is already done. Then substitute. ( ) 2x + (2x) = 8 4x = 8 x = 2 Substitute 2 back in for x in the easier equation!! y = 2x y = 2(2) y = 4 The solution to the system is (2, 4) Graph 2x + y = 8 -2x -2x y = -2x + 8 Graph y = 2x y = 2x. (2,4)

IV. Systems of Equations: Two lines in a coordinate plane can do two things: (1) intersect (perpendicular or not) (2) not intersect (parallel) SystemsAlgebraicGraph By Addition w/Multiplication 2x + y = 6 3x – 2y = 2 Graph 2x + y = 6 -2x -2x y = -2x + 6 y = 3/2x – 1 Graph 3x – 2y = 2 y = -2x + 6. (2,2) 7x = 14 x = 2 Substitute 2 back in for x in the easier equation!! 4(2) + 2y = y = 12 2y = 4 y = 2 The solution to the system is (2, 2) -8 -3x -3x -2y = -3x y = 3/2x – 1 ( )2 4x + 2y = 12

Given x and y intercepts: 1. x-int: 2 y-int: -3 (2,0) (0,-3) ● ● Notice that the slope is rise 3 run 2 or (2,0) (0,-3) (-3) 2 or y-int x-int. The y intercept (b) of -3 is given The equation in slope intercept form isy = 3 2 x opposite

Given Intercepts To write the equation in slope-intercept form use the pattern : y = y-intercept x-intercept x + y-intercept slope m b

Step 1: Compute slope Step 2: Use PS Form Step 3: Simplify to SI Form +2 y = 5/3x + 1/3 Using (1, 2) Part IV #1: Given 2 points.(1,2) and (4,7) You can check with other point: 7 = 5/3(4) + 1/3 7 = 20/3 + 1/3 7 = 21/3 7 = 7 check!

x = 8 Part VI #5: (8,7) and parallel to x = -2 x = 2 Part VI #6: (2,2) and perpendicular to y = 3 All vertical lines are parallel A vertical line is perpendicular to a horizontal line

Chapter 13 WS How can you get 100% on your final? Congrats two are locale speling be champien!