Topic 5 Coordinate geometry Flashcards
Parallel lines have the same ______.
gradient
Gradients of perpendicular lines = _______.
-1
If 3 or more points lie on the same straight line, we say they are ________.
If points A, B and C are collinear, then ________________.
We say they are collinear.
If points A,B and C are collinear then Gradient of AB = Gradient BC = Gradient AC
What is the formula for the coordinates of a midpoint of line segment?
coordinates of midpoint M =
( (x1 + x2)/2 , (y1 + y2)/2 )
What is the formula to find the distance between the two points?
square root of (x2 - x1) square + (y2 - y1) square
What is the Gradient-intercept form?
y = mx + c
What is the double-intercept form?
X/a + y/b =1
What is the general form?
ax + by + c = 0
Given gradient m and a point (x1,y1) on the line, find the equation of the line.
y - y1 = m(x -x1)
Given two points (x1,y1) and (x2,y2) on the line. Find the equation of the line.
Y - y1 = (y2 - y1)/(x2- x1) times (x - x1)
How should you find the area of plan figures?
Area of triangle ABC =
Half | x1 on top y 1 below x 2 on top y 2 below x 3 on top y3 below x1 on top y 1 below.
Take note to write this in an anti clockwise direction and make sure that you end the multiplication with the coordinates that you started multiplying with
What is the formula of the ratio theorem if the end of the line is x2, y2 and the start is x1 y1 and you want to find a random point on the line with one side of the line from x1y1 to the random point being m and the other side being n?
( (Nx1 + mx2)/(m + n), (ny1 + my2)/(m + n) )
What is the property of a parallelogram?
- It is a quadrilateral with two pairs of opposite sides parallel.
- The opposite sides of a parallelogram are equal in length.
- The opposite angles of a parallelogram are equal.
- The diagonals of a parallelogram bisect each other.
What is the property of rectangle?
- It is a parallelogram where all interior angles are right angles.
- It has the same properties as a parallelogram.
- The diagonals of a rectangle are equal in length.
What are the properties of a rhombus?
It is a parallelogram with all its sides equal in length.
The diagonals of a rhombus bisect each other at right angles.
The diagonals of a rhombus bisect the interior angles.
What is the property of a square?
It is a rhombus where all its interior angles are right angles.
The diagonals of a square are equal in length.
The diagonals are also perpendicular to each other.
What is the property of a kite?
It is a quadrilateral with two pairs of equal adjacent sides.
The longer diagonal bisects the other diagonal at right angle.
What is the property of a trapezium?
It is a quadrilateral with one pair of opposite sides parallel.
