MATHEMATICS

PS
PS
PS
2
y =
2
x + 1
y = x + 1
3
3
6 Show that the
y
area
=
2
enclosed
x + 1
3 y by 1the lines 3x
y = 1 −
3x
= −
2
The perpendicular
2 2
y = x + 1
, y = 1 −
3x
2
, 3y
− 2x
+ 1 = 0
bisector is the line
3y
− 2x
+ 1 = 0
at right angles to
and y = 21
y−+ 33x
x + 3y5− = 20x
+ 1 = 2y0+ 3x
+ 5 = 0
AB (perpendicular)
2
that passes though
forms
2y
+ 3x
+ 5 = 0
3y
− 2a xrectangle.
+ 1 = 0
the midpoint of AB
(bisects).
7 Find 2y
+ the 3x
equation + 5 = 0 of the perpendicular bisector of
each of the following pairs of points.
(i) A(2, 4) and B(3, 5)
(ii) A(4, 2) and B (5, 3)
(iii) A(−2, −4) and B(−3, −5)
(iv) A(−2, 4) and B(−3, 5)
(v) A(2, −4) and B(3, −5)
8 A median of a triangle is a line joining one of the vertices to the midpoint
of the opposite side.
In a triangle OAB, O is at the origin, A is the point (0, 6), and B is the point (6, 0).
(i) Sketch the triangle.
(ii) Find the equations of the three medians of the triangle.
(iii) Show that the point (2, 2) lies on all three medians. (This shows that
the medians of this triangle are concurrent.)
9 A quadrilateral ABCD has its vertices at the points (0, 0), (12, 5), (0, 10) and
(−6, 8) respectively.
(i) Sketch the quadrilateral.
(ii) Find the gradient of each side.
(iii) Find the length of each side.
(iv) Find the equation of each side.
(v) Find the area of the quadrilateral.
10 Afi rm manufacturing jackets finds that it is capable of producing
100 jackets per day, but it can only sell all of these if the charge to the
wholesalers is no more than £20 per jacket. On the other hand, at the
current price of £25 per jacket, only 50 can be sold per day. Assuming that
the graph of price P against number sold per day N is a straight line:
(i) sketch the graph, putting the number sold per day on the horizontal
axis (as is normal practice for economists)
(ii) find its equation.
Use the equation to find:
(iii) the price at which 88 jackets per day could be sold
(iv) the number of jackets that should be manufactured if they were to be
sold at £23.70 each.
5
Chapter 5 Coordinate geometry
15