Unit 3 lesson 7 the distance between two points and the angle between lines
Items in this lesson
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Welcome MYP5!
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Leerdoelen last week + self study
You can solve systems of linear equations.
You can work with the relative position of two lines
You can calculate the distance between two points
You know that for perpendicular lines, multiplying their slope ("richtingscoefficient") equals -1.
You can cross out exercise 10+ 11 from the booklet
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recap question
write down: what are the three different relative positions of lines?
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recap question
give two different linear equations (in the form px + qy = r)
decide what their relative position is
(hint: you may use the notes of last class!)
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recap question
when two lines are perpendicular (loodrecht), what do I know of their slopes (richtingscoefficient)?
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recap question
write down the formula for the distance between two points
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Recap: Relative position of lines
Three options
Basis boven:
AC=7
Basis onder:
GF=17.5
Schaalfactor:
17.5/7=2.5
De zijde AB=4 hoort bij GE.
Dus:
GE=4×2.5=10
Kleine driehoek rechts CDE is gelijkvormig met grote driehoek CFG.
CE/EF = CD/GF
2.5/EF = 2.5/17.5
Dus EF = 17.5
BF = BE+EF
Omdat BE = 2 -->
BF = 2 + 17.5 + 19.5
Recap: Relative position of lines
Lines
and system
The lines are secants and the system has one solution if
The lines are parallel and the system has no solution if
The lines are coicidential and the system has infinitely many solutions if
Basis boven:
AC=7
Basis onder:
GF=17.5
Schaalfactor:
17.5/7=2.5
De zijde AB=4 hoort bij GE.
Dus:
GE=4×2.5=10
Kleine driehoek rechts CDE is gelijkvormig met grote driehoek CFG.
CE/EF = CD/GF
2.5/EF = 2.5/17.5
Dus EF = 17.5
BF = BE+EF
Omdat BE = 2 -->
BF = 2 + 17.5 + 19.5
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Self study booklet: the distance between two points
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Recap: distance between points
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Self study booklet: perpendicular ("loodrechte") lines
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Recap: perpendicular lines and their slopes
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Leerdoelen today
You can calculate the distance from a point to a line
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Distance from a Point to a Line
Definition The distance from point P to line l equals the length of PP′, where P′ is the perpendicular projection of P onto l. Notation: d(P, l) = PP′
3-Step Method
Write the equation of line l through P, perpendicular to k.
Find the intersection point P' of k and l.
Use d(P, k) = d(P, P').
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3-Step Method
Write the equation of line l through P, perpendicular to k.
Find the intersection point P' of k and l.
Use d(P, k) = d(P, P').
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3-Step Method
Write the equation of line l through P, perpendicular to k.
Find the intersection point P' of k and l.
Use d(P, k) = d(P, P').
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Homework
Worksheet 3.4: distances in points and lines
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