Slide 1 :
Slide 2 :
Slide 3 : Pre-requisite Knowledge Distance Formula
Slope
Straight Line Drawing
Slide 4 : Review:Distance and Slope Equation of Straight Lines Points of Division Perpendicular and Parallel Lines Intersection of Two Straight Lines Contents
Slide 5 : Equation of Special Lines Two Point Form Point-Slope Form Slope-Intercept Form Intercept Form General Form Back =>
Slide 6 : Topic: Distance and Slope
(Review) Back=>
Slide 7 : y1 – y2 distance ? By Pythagoras Theorem, x1 – x2
Slide 8 :
Slide 9 : (a) Find AB if A=(4,0) and B=(9,a)
(Give the answer in terms of a.)
Slide 10 : x1 – x2 y1 – y2 slope ?
Slide 11 :
Slide 12 :
Slide 13 : If a line//x-axis
slope = 0
Slide 14 : If a line // y-axis
slope is undefined
Slide 15 : Back=> End of Topic
Slide 16 : Topic: Point of Division Back=>
Slide 17 :
Slide 18 : ? ?BCD ~?CAE
Slide 19 : C(x,y) 4 3 x = 3 x 8 + 4 x 1 3 + 4 y = 3 x 9 + 4 x 2 3 + 4
Slide 20 : What are the coordinates of P ? Ans: P = (2, 4)
Slide 21 : Find the values of a and b
Slide 22 : Solution
Slide 23 :
Slide 24 : Find the coordinates of point P
Slide 25 : Mid-Point Formula P is the mid-point of AB
Slide 26 : B (5, -2) (4, 1) Let P = (a, b) & G = (p, q)
Slide 27 : Given : G is the centroid
of ?ABC
Slide 28 :
Slide 29 :
Slide 30 : Let AP : PB = 1 : k Solution
Slide 31 : Topic: Equations of
Special Lines Back=>
Slide 32 : (1, 3) (-1, -3) x = -3 y = 3 y = -3 (2,1) y = 1
Slide 33 : (2, 2) (2, 0) (-3, -3) x = -3 x = 2 x = -1 x = -3
Slide 34 : (a, b) L2 L1 P Ans:
L1 : x = a L2 : y = b
P= (0, b) Find
The equations ofL1 and L2;
The coordinates of point P.
Slide 35 : y = x y =-2x
Slide 36 :
Slide 37 : Find the equations of L1 and L2.
Slide 38 :
Slide 39 : Topic: Two-Point Form Back=>
Slide 40 : Find the equation of L. MAP = MAB
Slide 41 : MBP = MAB
Slide 42 : (a) Find the equation of L. (b) Find the value of b. (c) Find the coordinates of P. L: 7x + 6y + 4 = 0
Slide 43 : (a) Find the equation of the straight line joining (-3, 2) and (2, -1). (b) Does the point (7, -4) lie on the straight line ? (c) State whether the point (3, -2) lies on the straight line or not. L: 3x - 5y + 1 = 0
Slide 44 : (a) Find the equation of the straight line which passes through (0,0) and (-4,-6). (b) If the point A(a,3) lies on L, find a.
Slide 45 : Back=> End of Topic
Slide 46 : Topic: Point-Slope Form Back=>
Slide 47 : Point-slope Form MAB = Slope
Slide 48 : Find the equation of the line which passes through (-1,-5) and has slope -3 : Solution
Slide 49 : (a) Find the equation of L. (b) What is the value of b ? Put B(2, b) into the equation L: x + 3y - 3 = 0
Slide 50 : Find (a) The equation of L.
(b) The coordinates of P
(c) The coordinates of Q
Slide 51 : Solution.
Slide 52 :
Slide 53 : Topic: Slope-Intercept Form
Slide 54 : L1 cuts the y-axis
at point (0,3) L1 cuts the x-axis
at point (-2,0)
Slide 55 : What is the equation of L ?
Slide 56 : (a) Find the equation of the straight line with y-intercept –1 and slope –3 in the slope-intercept form. y=?3x?1 Slope-intercept
Form
Slide 57 : L : kx + 3y – 2k = 0 with slope –2.
(a) Find the value of k .
Slide 58 : Ans.
Slide 59 :
Slide 60 : Topic: Intercept Form Back=>
Slide 61 : MAP = MAB What is the equation of L ?
Slide 62 : Find the equation of L in intercept form. Do the point (4, 6) and (12, 9) lie on L ?
Slide 63 : (a) Convert 7x + 4y + 28 = 0 into the intercept form. (b) What are the x-intercept and y-intercept of the straight line ? x-intercept = -4 and y-intercept = -7
Slide 64 : Find the area of the shaded region. The area of the shaded region is Intercept form
Slide 65 :
Slide 66 : Solution.
Slide 67 :
Slide 68 : Topic: General Form Back=>
Slide 69 : Ax + By + C = 0
Slide 70 :
Slide 71 : What are the slope and the y-intercept of the straight line 4x – 3y + 7 = 0 ?
Slide 72 : Find the equation of L in the general form.
Slide 73 : Find the x-intercept and the y-intercept of the straight line 12x – 7y + 4 = 0.
Slide 74 :
Slide 75 : Topic: Parallel Lines
and
Perpendicular Lines Back=>
Slide 76 : If L1 // L2 , then
mL1 = mL2 What will happen if
Two lines L1 and L2
Are parallel? A FACT to know... Conversely, if
mL1 = mL2
Then L1 // L2
Slide 77 : Determine whether L1 // L2 Since m1 = m2= 2, then, L1 is parallel to L2
Slide 78 : Find the equation of L2 mL2 = mL1 = 2
Slide 79 : (a) Find the equation of L2. (b) Does the point (-3, -5) lies on L2 ? L.H.S. = = 3(-3) + (-5) + 15
= 1
? R.H.S. Thus, (-3, -5) does not lie on L2
Slide 80 : Find the equation of L2. Step 1: Express L1 into slope intercept form. Step 2: Find the slope of L2 Step 3: Use point-slope form to find L2.
Slide 81 : Steps : 1. Express the given line into slope-intercept form.
2. Find the slope of L1.
3. Use point-slope form to find the equation of the line. Find the equation of the line L1 which is parallel to 3x + 2y – 5 = 0 and passes through (4, -1).
Slide 82 : Solution.
Slide 83 : If L1 ? L2 , then
mL1 x mL2 =-1 One more FACT... Conversely, if
mL1 x mL2 =-1
Then L1 ? L2
Slide 84 : Find the coordinates of P.(Hint: Let P = (a,0) thus, P = (-0.5, 0) ? L1 ? L2
? mL1 x mL2 =-1
Slide 85 : Find the equation of L2. Step 1: Express L1 into slope intercept form. Step 2: Find the slope of L2 Step 3: Use point-slope form to find L2.
Slide 86 : Steps : 1. Express the given line into slope-intercept form.
2. Find the slope of L.
3. Use point-slope form to find the equation of the line. Find the equation of the line L which is perpendicular to 3x - 2y + 6 = 0 and pases through (-4, 3).
Slide 87 : Solution.
Slide 88 :
Slide 89 :
Slide 90 : Find the equation of the perpendicular bisector of the line segment joining (3, -5) and (-7, 9). [ Ans.: 5x - 7y + 24 = 0 ] Steps : 1. Find the coordinates of the midpoint.2. Find the slope of the line segment. 3. Find the slope of the perpendicular bisector4. Use point-slope form to find the equation of the line.
Slide 91 : Topic: Point of Intersection
Slide 92 : What are the coordinates of P ? A. P = (-5, -7) B. P = (-5, 7) C. P = (5, -7) D. P = (5, 7) E. P = (7, 5)
Slide 93 :
Slide 94 :
Slide 95 : What are the coordinates of P ? A. P = (-5, 7) B. P = (5, 7) C. P = (7, 2) D. P = (7, 13) E. P = (13, 7)
Slide 96 : What are the coordinates of P ?
Slide 97 : The coordinates are (5, 4)
Slide 98 : P = (1, 2) What are the coordinates of P ?
Slide 99 :