Exam Style Questions B

	Exam Style Questions on Straight Lines
	Give answers to 2 decimal places


Q1	Line l₁ passes through the points A = ( 2, 0.5 ) and B = ( -1, 5 ).

	a)	Find the gradient of l₁				m =
	b)	Find the equation of l₁ in the form y = m x + c.

				y =		x +

		Line l₂ is perpendicular to l₁ and passes through B.

	c)	Give the equation of line l₂ in the form a x + b y + c = 0
		where a > 0, b and c are integers without common factors.

			a =		b =		c =


Q2	The triangle ABC has vertices as follows:

		A =	(1, 5)	B =	(4, -1)	C =	(-2, -4)

		Calculate:

	a)		The gradient of AB
	b)		The gradient of BC
	c)		The length of AB
	d)		The length of BC
	e)		The area of the triangle


Q3	Line l₁ passes through the points A = ( -5, 0 ) and B = ( 0, 3 ).

	a)	Give the equation of line l₁ in the form a x + b y + c = 0
		where a > 0, b and c are integers without common factors.

			a =		b =		c =

	b)	Line l₂ is perpendicular to l₁ and passes through ( 2, 11 ).
		Find the equation of this new line:

				y =		x +

	c)	Find the point of intersection of these two lines:

				x =		y =


Q4)	Line l₁ is given by the equation y = 3x + 7.
	Line l₂ is perpendicular to l₁ and passes through P = (-2, 3).

	a)	Write down the gradient of l₂
	b)	Hence find the equation of l₂.

				y =		x +

	c)	l₁ and l₂ cross the x axis at the points A and B respectively:

			x	y			x	y
		A =				B =

	d)	Calculate the length of the line PB:

			length PB =


Q5)	Line l₁ passes through the points A = ( -12, 0 ) and B = ( 0, 8 ).

	a)	Give the equation of line l₁ in the form a x + b y + c = 0
		where a > 0, b and c are integers without common factors.

			a =		b =		c =

	b)	M is the midpoint of AB and l₂ is perpendicular to AB and
		passes through M.

		Give the equation of line l₂ in the form a x + b y + c = 0
		where a > 0, b and c are integers without common factors.

			a =		b =		c =