Homework 1

	Homework 1 Straight Lines
	Give answers to 2 decimal places
			Your Score:

Q1	Line l₁ passes through the points A = ( -4, 12 ) and B = ( 3, -2 ).

	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 =	(-2, -8)	B =	(4, 4)	C =	(-4, 8)

		Calculate:

	a)	The gradient of AB
	b)	The gradient of BC
	c)	The length of AB (2 d.p.)
	d)	The length of BC (2.d.p.)
	e)	Area of the triangle (nearest whole number)


Q3	Line l₁ passes through the points A = ( -5, -2 ) and B = ( 8, 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 ( -4, 6 ).
		Find the equation of this new line:

				y =		x +

	c)	Find the point of intersection of these two lines. Give x to 2 d.p.
		Use your rounded answer to x when working out y.
				x =		y =


Q4)	Line l₁ is given by the equation y = 5x - 3.
	Line l₂ is perpendicular to l₁ and passes through P = (7, -8).

	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, answer to 2 d.p.

			length PB =


Q5)	Line l₁ passes through the points A = ( -4, 6 ) and B = ( 7, -4 ).

	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 =