Parallel and perpendicular lines in linear functions

Parallel and perpendicular lines in linear functions

Parallel lines are lines with identical slope. In other words, these lines will never cross each other. Perpendicular lines will always pass through each other and form right angles at the interception. In this lesson, we will learn how to use information such as, points in lines and their slopes, to determine whether the lines are parallel, perpendicular or neither.
Basic concepts: Slope equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}, Slope intercept form: y = mx + b, Point-slope form: y−y1=m(x−x1)y - y_1 = m (x - x_1),
Related concepts: Parallel line equation, Perpendicular line equation, Combination of both parallel and perpendicular line equations,

Lessons

Parallel
lines− - identical slope so they never intersect each other, unless overlapped.

Perpendicular
lines− - two lines form right angles to each other when they intersect. If the slope of first line is ab {a \over b} , the slope of perpendicular line is the slope of perpendicular line is −ba - {b \over a} . The product of the two slopes is -1.
  • 1.
    Determine whether the three points A (-2,-1), B(0,4) & C(2,9) all lie on the same line.
  • 2.
    Determine the following slopes are parallel, perpendicular, or neither.
    i) m1=25,m2=25 m_1 = {2 \over 5}, m_2= {2 \over 5}

    ii) m1=15,m2=−51m_1 = {1 \over5} , m_2 = - {5 \over 1}

    iii) m1=47,m2=1221m_1 = {4 \over 7}, m_2 = {12 \over 21}

    iv) m1=m_1 = undefined, m2=0 m_2 = 0

    v) m1=mn−1;m2=−m−1bm_1 =mn^{-1}; m_2 =-m^{-1}b
  • 3.
    Given the points of two lines, determine when the lines are parallel, perpendicular or neither.
    a)
    Line 1: (3,2) & (1,4); Line 2: (-1,-2) & (-3,-4)

    b)
    Line 1: (5,6) & (7,8); Line 2: (-5,-6) & (-7,-8)

    c)
    Line 1: (0,4) & (-1,2); Line 2: (-3,5) & (1,7)

  • 4.
    Show that the points A(-3,0), B(1,2) and C(3,-2) are the vertices of a right triangle.
  • 5.
    Show that the points A(-1,-1), B(3,0), C(2,4) and D(-2,3) are the vertices of a square.
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12.
Linear Functions
12.1
Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}
12.2
Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)
12.3
Gradient equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}
12.4
Gradient intercept form: y = mx + b
12.5
General form: Ax + By + C = 0
12.6
Gradient-point form: y−y1=m(x−x1)y - y_1 = m (x - x_1)
12.7
Rate of change
12.8
Graphing linear functions using table of values
12.9
Graphing linear functions using x- and y-intercepts
12.10
Graphing from gradient-intercept form y=mx+b
12.11
Graphing linear functions using a single point and gradient
12.12
Word problems of graphing linear functions
12.13
Parallel and perpendicular lines in linear functions
12.14
Applications of linear relations
NZ Year 10 Maths
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