Analytical Geometry

Question 1

What do we know about the gradients of two parallel lines?

Answer 1

They are equal.

Question 2

What do we know about the gradients of lines that are perpendicular?

Answer 2

Their product are equal to -1.

Question 3

What are the 4 properties of a parallelogram?

Answer 3

1 - Both pairs of opposite sides are equal
2 - Both pairs of opposite sides are parallel
3 - Both pairs of opposite angles are equal
4 - The diagonals bisect each other

Question 4

What are the steps involved in calculating the equation of a straight line?

Answer 4

Step 1: Determine the gradient of the line
Step 2: Calculate the y-intercept by substituting the x and y values of a point lying on the straight line in the equation y = mx + c

Question 5

What is the relationship between the inclination angle of a straight line and its gradient?

Answer 5

tan @ = m

Question 6

What are the properties of a kite?

Question 7

How do you prove that a quadrilateral is a parallelogram/kite/rhombus..etc?

Answer 7

Step 1: List out all properties of the quadrilateral in question.
Step 2: Prove that the quadrilateral in question exhibits those properties.

Question 8

How do you determine the length of a line segment?

Answer 8

By using the distance formula. Alternatively, you can use the theorem of pythagoras if the line segment is part of a right-angled triangle.

Question 9

What do we know about the gradients of collinear points?

Answer 9

Gradients are equal

Question 10

What do we do as a final step in calculating the angle of inclination of a straight line with a negative gradient

Answer 10

We add 180 degrees to the negative angle found by solving the equation tan @ = m.