Sunday, July 08, 2007

Introduction to Coordinate Geometry

In the learning of coordinate geometry, alot of emphasis has been placed on the more abstract concepts of the topic. For instance, students are required to formulate the equation of a line from 2 points, or the gradient of a line. However, students may not have adequate understanding about the concept of the properties of a straight line. For example, what is the significance of gradient and y-intercept? Why do we need to formulate equations of lines? But most importantly, what is the use of graphs? An a example is given below to illustrate the significance of gradient and y-intercept in everydaylife.An experiment was conducted to find the speed of tennis ball in air and a distance time graph is found using experimental tools like a data logger:
From the graph, we see that the distance travelled by the ball is linearly related to the time taken. Consider the gradient in this case. How would the graph of the slow and fast moving tennis ball differ?

The gradient of the graph represents the speed of the ball, as the gradient measures the change in distance over the change in time. In other words,

gradient = rate of change of distance= speed

Hence, there is a physical intepretation of gradient of the line in this case.
From the graph, we also see that the ball does not start from rest. What is the distance travelled by the ball when the timer was started? In this case,

y-intercept = distance travelled by ball at the 0 sec

Hence there is also a physical intepretation for the y- intercept of the line.


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