Coordinate Geometry
Clement Radcliffe, Contributor

The solution to the following problem will vomplete the review of the aspects of coordinate geometry which we shared during the last three weeks.

PROBLEM

E is the point (-2,5) and F is the point (2,-3). Find by calculation:

(i) The coordinates of G, the midpoint of EF
(ii) The gradient of EF
(iii) Detremine the equation of the perpendicular bisector of EF

SOLUTION

(1) Since G is the midpoint of E (-2,5) F (2,-3)

(ii) The perpendicular bisector of EF passes through G (0,1) and has gradient perpendicular to EF.

If this line has gradient m1, then m1 x - 2 = -1

The product of the gradients of perpendicular lines is equal to -1.

ie. The equation of the perpendicular bisector of EF is: 2y = x + 2

Let us now proceed to review VECTORS.

Please review the following description:

(a) A motor car travels with velocity 45Km per hour due north
(b) A force of 25 N due East.

Could you say what both statements have in common?

You are correct that in both cases, their sizes and directions are given, These are examples of vector quantities representing velocity of a car and force respectively.

A vector quantity is one which identifies both the magnitude (size) and direction, for example, velocity given above.

A speed of 20 metres per second is a scalar quantity. (No direction given)

Vector quantities are usually represented in the form:

POINTS TO NOTE

(a) Avoid making the common error of interchanging x and y values.

(b) If the coordinates of A (x1, y1) and B (x2, y2) are given then x = x2 - x1 and y = y2 - y1

It is clear that the negative sign reverses the direction of the vector.

Please attempt the following for Homework.

* Clement Radcliffe is principal of Glenmuir High School in Clarendon.