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bio_man bio_man
wrote...
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Educator
Posts: 33342
3 years ago
A piece of broken plate was dug up in an archeological site. It was put on top of the grid where the arc of the plate passes through the points X(1,1), Y(1,7), Z(4,4). What is the diameter of the wheel?
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bio_man Author
wrote...
Educator
3 years ago
Notice that point X and Y both have the same x-coordinate. Let's assume we're dealing with a circle here.

Therefore, they exist on opposite sides of the circle. In fact, connecting point X and Y creates a line-segment that is also the diameter of the circle, shown below for reference.



By finding the distance from X to Y, then dividing by 2, we will have found the diameter, and subsequently the radius.

d=(x2x1)2+(y2y1)2
X=(1,1);Y=(1,7)
d=(11)2+(71)2
d=36
d=6

Diameter is 6, therefore the radius is 3. Since X and Y are along the same plane, add 3 to 1 (1 being the y-coordinate of X). Therefore, the radius is at (1,4).

The equation for the circle, therefore is:

x2+y2=r2
(x1)2+(x4)2=32

To test the third point Z, simply apply its coordinates into X and Y to check if it equals 9. It should...

Good luck Slight Smile
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