Possible Final Exam Question Midpoint formula: Midpoint of a Line Segment M = A waste management company is planning to build a landfill in a rural area. To balance the impact on the two closest towns, the company wants the landfill to be the same distance from each town. On a coordinate map of the area, the towns are at A (1,8) and B (5,2). Describe the possible locations for the landfill Distance formula can be used to find the length of a line segment Finding Length of a Line Segment Equation of a circle with center (0,0), which is the origin. Equation of a Circle note that the slope of parallel lines are the same while the slope of perpendicular lines are negative reciprocal. Classifying Figures on a Coordinate Grid Triangle has vertices A(-2,2), B(-1,-3) & C(4,1). Show that the line segment joining the midpoints of AB & AC is parallel to BC Using Coordinates to Solve Problems You can find the midpoint of this line segment by using the formula. median: A line that is drawn from a vertex of a triangle to the midpoint of the opposite side median the equation for a median can be determined by using midpoint formula, slope and equation of the line note that the equation of the line: y=mx + b M Perpendicular bisector: a line that bisects a line segment and is perpendicular to the line segment perpendicular line To calculate, use negative reciprocal M = 1 + 5 , 8 + 2

----- -----

2 2 M = 6/2 , 10/2

M = ( 3 , 5 ) m = 2 - 8

-------

5 - 1 m = -6

---

4 = -3

---

2 negative

reciprocal y = 2/3x + b

5 = 2/3(3) + b

5 = 2 + b

5 - 2 = b

3 = b y=2/3x + 3 (1,8) (5,2) possible landfills; (6,7) or (0,3) D = Example: A fishing boat sends a distress signal from a location given by the coordinates (200,180). An ocean freighter at coordinates (170,240) and a cruise ship at coordinates (230, 180) pick up the distress signal. Which ship is closer to the fishing boat? D = ocean freighter D = (170 - 200) + (240 - 180) 2 2 D = (-30) + (60) 2 2 D = -900 + 3600 D = 4500 D = 67.082 Cruise Ship D = D = (200 - 230) + (180 - 180) D = (30) + (0) D = 900 + 0 D = 900 D = 30 Therefore, the cruise ship is closer 2 2 2 2 x + y = r 2 2 2 If the value of r is given use the formula; x + y = r 2 2 Example: r=2 x + y = 2 x + y = 4 Example: x + y = 49 r = 49

r = 7 2 2 2 2 2 2 2 2 You must know the characteristics and properties of triangles and quadrilaterals in order to determine the geometric figure. Determine if the quadrilateral with vertices A(1,6), B(9,5), C(11,1), and D(3,2) is a parallelogram To determine, you must calculate the slope of AB, CD, AD, and BC. and then determine their distance length. If the slope and length of the opposite sides are the same, the quadrilateral is a parallelogram. To solve, you must find the midpoint of AB and AC. Then,calculate the slope of the line segment and slope of BC. If they have the same slope, then the line segment is parallel to BC Chapter 2 Find the shortest distance from point D(8,3) to the line segment joining points A(1,-8) and B(-4,2). To find the shortest distance, you must determine the midpoint of line segment AB. calculate the distance of the perpendicular line Shortest distance is 11.24 units.

### Present Remotely

Send the link below via email or IM

CopyPresent to your audience

Start remote presentation- Invited audience members
**will follow you**as you navigate and present - People invited to a presentation
**do not need a Prezi account** - This link expires
**10 minutes**after you close the presentation - A maximum of
**30 users**can follow your presentation - Learn more about this feature in our knowledge base article