Chapter 1: Orienting Yourself: The Use of Coordinates

Exercise

Question

Question: 15 (ii)

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A computer graphics program displays images on a rectangular screen whose coordinate system has the origin at the bottom-left corner. The screen is 800 pixels wide and 600 pixels high. A circular icon of radius 80 pixels is drawn with its centre at the point A (100, 150). Another circular icon of radius 100 pixels is drawn with its centre at the point B (250, 230). Determine:

(ii) whether the two circles intersect each other.

Answer

1
Find the distance between the centres of the two circles, A (100, 150) and B (250, 230).
AB = \sqrt{(250 - 100)^2 + (230 - 150)^2} = \sqrt{150^2 + 80^2} = \sqrt{22500 + 6400} = \sqrt{28900} = 170 pixels
2
Find the sum of the radii of the two circles.
r_A + r_B = 80 + 100 =180 pixels
3
Compare the distance between the centres with the sum of the radii. If the distance is less than the sum of the radii, the two circles intersect.
Answer: Yes. The two circles intersect.
Reason: The distance between their centres is 170 pixels, which is less than the sum of their radii, 180 pixels. Therefore, the two circles intersect.
Coordinate screen showing two intersecting circles centred at A (100, 150) and B (250, 230).
The two circles intersect at two points.
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