Rania Ali was pleased at success of the Giant Graph Graffiti project, particularly because the grade 10 students were heavily involved in it. She thought that this would have brought the idea of co-ordinates into their thought proces. Now she could continue with the next co-ordinate geometry lesson. Instead, she just wrote two equations on the board.
Equation 1. 2x + y = 8
Equation 2. x − y = 1
The students were confused. She even heard Mehak and Arisha whispering that this was a geometry period and not a class for algebra equations. Nevertheless, one of the students used the substitution process, solved the equations algebraically and showed the work to Rania Ali.
Rania Ali sent the student back and announced that Mehak had thought that this was a geometry period. Therefore, they will have to solve the equations using geometry. Then she called Rajab to write on the board the values of y for different values of x.
…
Taheen: Can I draw the XY coordinates on the board?
Rania Ali: Yes, please draw the XY coordinates and also a line connecting the Equation 1 coordinates that Rajab has written.
Rania Ali: As you can see this blue line represents the geometrical form of Equation 1. Taheen, now draw the line for Equation 2.
Rajab: We need to find a point which satisfies both Equations 1 and 2. Taheen, can you draw both the lines on the same graph?
Taheen: Okay, I will do that.
Rajab: The two lines cross at x = 3 and y = 2. So that is the answer.
The student who had solved the equations by substitution announced that he got the same answer.
Rania Ali: You can also verify the answers by substituting x and y values in the two equations. Equation 1. 2x + y = 8 and 2 × 3 + 2 = 8.
Raania Ali continued: Today we used coordinate geometry to solve two linear equations. As you continue your study of mathematics, you will discover that co-ordinate geometry can also be used with many other kinds of equations.
Challenge
Draw a circle with a center at x = 3, y=2 and a radius of 4.
Solution
A circle has a center and a radius. The equation of this circle is
(x – 3)2 + (y-2) 2 = 42
Below is the graph for this equation for the circle.
Math Stories For You 