Lesson 1 - Lines:Slopes, Distances, Midpoints

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Lesson 1 - LinesSlopes, Distances, Midpoints

• Functions Trig - Santowski

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(A) Slope

• Given the 2 points (x1,y1) and (x2,y2), the
  slope of a line is determined using the formula

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(A) Horizontal and Vertical Lines

• Find the slope of the line going through the
  points A(2,5) and B(-4,5)
• If a line is horizontal, then its slope is 0
• Find the slope of the line going through the
  points A(2,5) and B(2,-4)
• If a line is vertical, then its slope is undefined

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(A) Slope

• The slope of a line then implies an average rate
  of change between 2 points

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(B) Examples

• Ex 1. A line segment goes through the points
  A(2,-3) and B(-1,5). Determine the slope of the
  line segment
• Ex 2. In 1990, the population of Doha was
  250,000. In 2005, the population of Doha was
  850,000. Find the average rate of change of
  population in Doha between 1990 and 2005

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(C ) Parallel and Perpendicular Lines

• If two lines are parallel, then their slopes are
  equal
• If two lines are perpendicular, then there slopes
  are negative reciprocals of each other

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(D) Examples

• Ex 1. Line 1 passes through A(2,4) and B(-1,5).
  Line 2 passes through C(-3,-1) and D(2,-1). Line
  3 passes through E(3,1) and F(-1,-3). Which two
  lines are parallel? Perpendicular? or neither?
  How do you know.
• Ex 2. If Line 4 has an x co-ordinate of 5, what
  must its y co-ordinate be in order for Line 4 to
  be (i) parallel with and (ii) perpendicular to
  one of the lines in Ex 1.

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(E) Length of a Line Segment

• Given the 2 points (x1,y1) and (x2,y2), the
  length of the line segment between the 2 points
  is determined using the formula

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(F) Examples

• Ex 1. A line segment goes through the points
  A(2,-6) and B(-1,5). Determine the length of the
  line segment.
• Ex 2. Doha and Abu Dhabi are located on map at
  the co-ordinates given by D(2,3) and AD(4,-1). If
  one unit on the map corresponds to 20 miles, how
  far apart are Doha and Abu Dhabi?

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(G) Midpoint of a Line Segment

• Given the 2 points (x1,y1) and (x2,y2), the
  midpoint of the line segment between the 2 points
  is determined using the formula

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(H) Examples

• Ex 1. A line segment goes through the points
  A(12,-3) and B(-1,15). Determine the midpoint of
  the line segment
• Ex 2. Two towns are located at T(-12,30) and
  F(15,3) on a coordinate grid. Find the location
  of an airport that is located halfway between the
  two towns. If one unit on the grid represents 3
  miles, how far is each town from the airport?

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(I) Homework

• Section 1.1, p5-7, Q2,4,6,19,20
• Section 1.2, p11-13, Q2,4,6,12,14,16-20
• Then Complete the tasks for Lesson 1 as outlined
  on the Task Sheet