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Content
Content
- Distance Between Two Points
- Mid Point
- Gradient of Straight Line
- Collinear Points
- Parallel and Perpendicular Lines
- Equation of Vertical and horizontal Lines
- Equation of a straight line
- What You need To Find Equation of a Straight Line?
Distance Between Two Points
Distance Between Two Points
The distance between two points (x1,y1) and (x2,y2) is
Coordinate of Midpoint
Coordinate of Midpoint
Find the coordinate of the midpoint between (2 , 3) and (4 , 7).
Gradient of a Straight Line
Gradient of a Straight Line
Find the gradient of a straight line passing through (3, 4) and (5, 9).
Gradient = (y2 – y1) / (x2 – x1)
= (9 – 4) / (5 – 3)
= 5 / 2
= 2.5
Collinear Points
Collinear Points
Three Points A,B,C are Collinear, if they lie on the same straight line.
Gradient AB = Gradient BC.
Find y, if A(2 , 3), B(4 , 5) and C(7 , y) are collinear.
If A, B and C are collinear, Gradient AB = Gradient BC.
(5 – 3) / (4 – 2) = (y – 5) /(7 – 4)
2/2 = (y – 5) /3
1 = (y – 5) /3
1 x 3 = (y – 5)
3 = y – 5
3 + 5 = y
y = 8
Parallel and Perpendicular Lines
Parallel and Perpendicular Lines
If two lines are parallel, then they have equal gradients.
If two lines are perpendicular, then multiplication of their gradients equals – 1.
Equation of Vertical and horizontal Lines
Equation of Vertical and horizontal Lines
Equation of vertical line is x = a, a is x-intercept.
Equation of horizontal line is y = b, b is y-intercept.
Equation of a straight line
Equation of a straight line
y= mx + c
m is the gradient
c is the y-intercept, where the line cuts the y axis.
What You need To Find Equation of a Straight Line?
What You need To Find Equation of a Straight Line?
- gradient and y-intercept (or)
- Gradient and coordinate of one point on the straight line (or)
- Coordinates of two points on the straight line (or)
- Equation of a Parallel/perpendicular line and
- y-intercept (or)
- Equation of a Parallel/perpendicular line and coordinate of one point on the straight line.
Find Equation of Straight Line with gradient is 2 and passing through (3,2).
y = mx + c
y = 2x + c
Since the line passing through (3,2), substitute x = 3 , y = 2
2 = 2(3) + c
c = – 4
Hence the equation of the line is y = 2x – 4.
Find Equation of Straight Line Passing through (2 , 3) and (4, 6).
Gradient = m = (6-3) / (4-2) = 1.5
y = 1.5x + c
Since the line passing through (2 , 3), substitute x = 2 , y = 3
3 = 1.5(2) + c
c = 0
Hence the equation of the line is y = 1.5x.
Find Equation of Straight Line Parallel to y = 5x + 10 and passing through (2 , 3)
Since the lines are parallel, their gradients are equal.
m = 5
y = 5x + c
Since the line passing through (2 , 3), substitute x = 2, y = 3
3 = 5(2) + c
3 = 10 + c
c = – 7
Hence the equation of the line is y = 5x – 7.
Finding Equation of Straight Line Perpendicular to y = – 3x + 7 and passing through (3 , 2)
Since the lines are perpendicular, m = 1/3
y = (1/3) x+ c
Since the line passing through (3,2), substitute x = 3 , y = 2
2 = (1/3) (3) + c
c = 1
Hence the equation of the line is y = (1/3) x + 1
Multiply by 3, 3y = x + 3.
Question
Question
- Find the gradient of the line 8y = 4x + 5
- Find the value of m if the point (m, m+2) lies on the line 2y = 3x – 9
- A(1,3) and B(10,12). Find (a) Length of AB (b) Mid-point of AB (c) Equation of AB.
- Find the equation of the line parallel to x-axis and passes through the point (2 , 4).
- Find the equation of the line parallel to y-axis and passes through the point (–6 , –3).
- Find the equation of the line that is parallel to y = 2x + 5 and passes through the point (1 , 5).
- Find the equation of the line that is parallel to y = –6x + 12 and passes through the point (6 , 2).
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