3.01 – Review of Lines Flashing Back to Grade 10

Goals for this Mini-Unit Be able to find the equation of a line through two points Know how parallel and perpendicular lines are related Find the intersection of lines Prove that line segments form certain geometric shapes

Goals for this Mini-Unit Relate line segments to chords of circles Find the centre of a circle Find the radius of a circle Apply the distance and midpoint formulae in circles

Review of Lines Every straight line follows the equation y = mx + b m is the slope – a measure of how steep the line is m = rise = Δ y run Δ x b is the y-intercept

Finding the Eq’n of a Line If a line has a slope of -3 and passes through the point (8, 1), what is its equation? y = -3x + b 1 = -3(8) + b 1 = b  b = 25 y = -3x + 25

Finding the Eq’n of a Line A line passes through the points (3, 2) and (9, 12). Find its equation.

Working with Slopes The symbol || means ‘parallel’ Parallel lines are always the same distance apart; they never touch; their equations have the same slope The lines y = 2x + 10 and y = 2x – 5 are parallel – we can tell because they both have a slope of 2.

Working with Slopes The symbol ┴ means ‘perpendicular’ Perpendicular lines intersect (cross) at right angles; their equations have slopes which are negative reciprocals The lines y = ¼x – 20 and y = -4x + 1 are perpendicular, because ¼ and -4 are negative reciprocals of each other.

A Note on Naming Typically in this unit we will be dealing with line segments rather than lines. These are distinguished by putting a line over the two letters representing its endpoints. Often you will find several slopes – use subscripts to keep them identified.

Example Refer to p. 222 of the textbook – we are going to do #1 as an example. Our first step is to plot GOLD to see which sides ought to be parallel, and which are perpendicular.

G O L D

Example We expect GO to be parallel to LD Same slope, they are parallel

Example We also expect OL to be parallel to GD. Same slope, they are parallel

Example In finding these 4 slopes, we can also show that adjacent sides are perpendicular. is the negative reciprocal of Adjacent sides are therefore ┴