Geometry

Question 1

How do you find the angle between a line and the x-axis?

Answer 1

tan^-1(m) = angle

Question 2

How do you find the equation of a line if you have the gradient and a point it passes through?

Answer 2

y - y(1) = m(x - x(1) )

        m = the gradient (x(1) , y(1) ) = the point

Question 3

How do you find the equation of a line that passes through two points?

Answer 3

y - y(1) y(2) - y(1)
———— = ————–
x - x(1) x(2) - x(1)

Question 4

How do you find the shortest distance between a point and a line?

Answer 4

[ax(1) + by(1) + c]
d = ———————–
________
+\/ a^2 + b^2

Question 4

How do you find the equation of a line passing through a point and the point of intersection?

Answer 4

(a(1)x + b(1)y + c(1) ) + k(a(2)x + b(2)y + c(2) ) = 0

Substitute in the x and y of the point and solve for k.
Substitute in k in then solve for x and y.

Question 5

How do you prove that a parabola is positive definite?

Answer 5

Prove the leading coefficient is positive and the discriminant is negative.

Question 6

How do you prove that a parabola is negative definite?

Answer 6

Prove that both the leading coefficient and the discriminant are negative.

Question 7

How do you find the maximum or minimum of something?

Answer 7

Create an equation with only one unknown for the thing that is being maximised or minimised.
Find the derivative of the equation.
The value of the unknown is the min or max.

Question 8

When proving that two quadratics are identical, what must you prove and what sign do you use?

Answer 8

You must prove the coefficients are equal.

Use the congruency sign (three horizontal lines).