Co-ordinate geomtry Flashcards
(13 cards)
What is the formula for the distance between two points?
sqrt[(x1 - x2)^2 + (y1 - y2)^2]
This formula calculates the straight-line distance in a Cartesian coordinate system.
How do you find the midpoint between two points?
[ (x1 + x2) / 2 ], [ (y1 + y2) / 2]
The midpoint is the average of the x-coordinates and y-coordinates of the two points.
What is the formula for the gradient of a straight line?
m = [(y2 - y1) / (x2 - x1)]
The gradient (slope) indicates the steepness of the line.
What is the general equation of a line?
y = mx + c
In this equation, m is the gradient and c is the y-intercept.
What does ‘c’ represent in the equation of a line?
y-intercept
The y-intercept is the point where the line crosses the y-axis.
What is the equation of a parallel line?
y = mx + c
The slope m remains the same as the original line; c is determined using provided points.
What is the equation of a perpendicular line?
y = m2x + c
The product of the slopes of two perpendicular lines (m1 and m2) is -1.
What is the formula for the area of a triangle?
A = 0.5 x b x h
Here, b is the base and h is the height of the triangle.
What is the general equation of a circle?
x^2 + y^2 + 2gx + 2fy + c = 0
This equation can be used to derive the center and radius of the circle.
How do you find the center of a circle from its equation?
Centre at (-g, -f)
The center is derived from the coefficients of the circle’s equation.
What is the formula for the radius of a circle?
radius = sqrt(g^2 + f^2 - c)
The radius can be calculated using the center and the constant term in the circle’s equation.
What is another form of the equation of a circle?
(x - a)^2 + (y - b)^2 = r^2
In this form, (a, b) represents the center and r is the radius.
What concept involves the relationship between a graph and its algebraic equation?
Understanding the relationship between points of intersection of graphs and solutions of equations
This includes the connection between tangents to curves and repeated roots of equations.
