Take the origin O(0, 0) on graph paper as the centre and draw a circle with a pair of compasses and a pencil.
Take a point P(x, y) on the circumference of the circle.
Mark other points \( P_1(x, y), P_2(x, y), P_3(x, y), \ldots \) on the circle.
Join the centre O to P and to each of the other points.
The line OP is the radius of the circle, written r. Take O(0, 0) = \( (x_1, y_1) \) and P(x, y) = \( (x_2, y_2) \), and use the distance formula to fill in the empty places in the table.
No.
Distance squared
Putting in the coordinates
Simplified
1
\( OP^2 = r^2 = (x_2 - x_1)^2 + (y_2 - y_1)^2 \)
\( r^2 = (x - 0)^2 + (y - 0)^2 \)
\( r^2 = x^2 + y^2 \)
2
\( OP_1^2 = r^2 = \)
3
\( OP_2^2 = r^2 = \)
4
\( OP_3^2 = r^2 = \)
Discussion
Do \( OP^2, OP_1^2, OP_2^2 \) and \( OP_3^2 \) all give the same result? Discuss.
Measure OP, \( OP_1 \), \( OP_2 \) and \( OP_3 \) in your figure. Write their lengths. Are they equal?
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