Analytical Geometry Flashcards
Altitude?
A line drawn from a vertex perpendicular to opposite side
Lines that are perpendicular to one another’s gradients…?
Will give -1 when multiplied
Parallel lines have the same…?
Gradient
Properties of a parallelogram?
- Both pair opposite sides //
- Both pair opposite sides =
- Diagonals bisect
- Opposite angles =
- 1 pair opposite sides = and //
What’s the easiest way to prove a quadrilateral is a parallelogram, assuming you have the coords of each point?
Use the midpoint formula - M((x1 + x2)/2, (y1 + y2)/2) - to prove that the diagonals bisect eachother.
How do you determine the 4th point of a parallelogram?
By inspection - analyse the change in x/y values across the 3 points you have. Give the reason ‘inspection’
What is the angle of inclination?
The angle on the right created by a line intersecting a horizontal line (like the x axis).
Use tanθ = gradient to find the angle.
Be careful when there’s a negative gradient - leave it out on the calculator and ensure the answer is the angle you’re looking for.
Properties of a square?
- = sides
- = angles (90 degrees)
- diagonals =
Properties of a rectangle?
- opp sides =
- angles = (90 degrees)
- diagonals =
Properties of a kite?
- 2 pairs adjacent sides equal
- 1 pair opposite angles equal (angles
between unequal sides) - The diagonal between equal sides
bisects the other diagonal - The diagonal between equal sides
bisects the interior angles - The diagonals intersect at 90°
Properties of a trapezium?
One pair of opposite sides parallel
Properties of a rhombus?
- All the properties of a parallelogram+ :
- All 4 sides equal
- Diagonals bisect each other at 90°
- Diagonals bisect both pairs of opposite angles
What is a median?
A line drawn from vertex to midpoint of opposite side.
What is a perpendicular bisector?
A line that intersects with another at a 90 degree angle at the midpoint.
