Straight Line Flashcards
Lines with equal gradient are…
Parallel
What is the gradient of a horizontal line
m = 0
What is the gradient of a vertical line?
m is undefined
What is the gradient formula?
A line with zero gradient is…
Horizontal (parallel to the x axis)
Parallel lines have…
Equal gradient
How do you find the equation of a straight line?
- Find the gradient
- Need to know a point on the line (a, b)
- Sub into y - b = m( x - a )
How do you find the mid point of a line?
What is the rule for perpendicular lines?
What is the distance formula?
What is a median of a triangle?
Median is a line drawn from one vertex to the midpoint of the opposite side
What is an altitude of a triangle?
Altitude is a line through a vertex, perpendicular to the
opposite side.
What is a perpendicular bisector?
A line which bisects (cuts in half) a given line at right-angles
How do you find the equation of a median
through a point of a triangle?
- Draw a sketch
- Find the midpoint required
- Find the gradient from the vertex to the midpoint
- Use y – b = m( x – a )
How do you find the equation of an altitude of a triangle through side BC?
- Draw a sketch
- Find the gradient of BC
- Use m1 x m2 = -1 to find
gradient of the altitude - Use y – b = m (x – a)
How do you find the equation of a perpendicular bisector?
- Draw a sketch
- Find midpoint of AB
- Find gradient of AB
- Use m1 x m2 = -1 to find gradient of perpendicular bisector CD
- Use y – b = (m – a )
How do you know if a point lies on a line or curve?
Substitute the x and y coordinates of the point into the equation of the line or curve. If the L side = R side, then the point does lie on the line.
How do you know 3 lines are concurrent?
For three lines to be concurrent, they must all pass through a single point.
___________________________
Find where 2 lines intersect and sub x and y into 3rd. If Left = Right, then lines are concurrent
How do you find the size of the angle between a line and the x-axis?
How do you show that the points A, B and C are collinear?
- Show that mAB = mBC
- State that the two line segments AB and BC have a common point B
What does it mean if three points are said to be collinear?
The lie on the same straight line and share a common point
What is the equation of this line?
x = -2
What is the equation of this line?
y = 4
How to you find the gradient of a line in the general form Ax + By + C = 0
Rearrange into y = mx + c
How to you find the point where a line cuts the x axis?
Set y = 0
How do you find the point where a line cuts the y axis?
Set x = 0
How to you find the point where two lines intersect?
Use simultaneous equations
