Coordinate Geometry Flashcards
What is the gradient formula between two points (x₁, y₁) and (x₂, y₂)?
m = (y₂ - y₁) / (x₂ - x₁)
What is the equation of a straight line in slope-intercept form?
y = mx + c
What is the condition for two lines to be parallel?
They have the same gradient.
What is the condition for two lines to be perpendicular?
The product of their gradients is -1.
How do you find the midpoint of a line segment?
Midpoint = ((x₁ + x₂)/2 , (y₁ + y₂)/2)
How do you find the distance between two points?
Use the distance formula: √[(x₂ - x₁)² + (y₂ - y₁)²]
What is the general form of a straight line?
Ax + By + C = 0
How do you find the equation of a line given a point and gradient?
Use y - y₁ = m(x - x₁)
What does the gradient represent?
The rate of change or steepness of the line.
What is the gradient of a vertical line?
Undefined.
What is the gradient of a horizontal line?
Zero.
How do you find the point of intersection between two lines?
Solve the two equations simultaneously.
How do you determine if a point lies on a given line?
Substitute the point into the line equation and check if it satisfies it.
What is the meaning of collinear points?
Points that lie on the same straight line.
What does it mean geometrically if three points are collinear?
The gradient between any two pairs of the points is the same.
How do you find the equation of a perpendicular bisector?
Find the midpoint, calculate negative reciprocal of gradient, then use y - y₁ = m(x - x₁).
What does the intercept ‘c’ represent in y = mx + c?
The y-coordinate where the line crosses the y-axis.
What is a locus in coordinate geometry?
A set of points satisfying a given condition.
What is the vector form of a line between two points A and B?
r = a + λ(b - a), where λ ∈ ℝ.
What is the Cartesian form of a line from a vector equation?
Convert r = a + λd into x = …, y = … by equating components.
