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ionmjnm9701
04.12.2021 •
Mathematics
Find the distance bewteen points H(8,4) and k(7,6) to the nearest hundreath
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Ответ:
Part 1) The diameter is
and the radius is equal to ![r=3\ units](/tpl/images/0005/1449/e2184.png)
Part 2) The center of the circle is (1+6i)
Part 3) The point (1+9i) lies on the circle
Part 4) The point (2-i) does not lies on the circle
Step-by-step explanation:
Part 1) Show me how you would determine the length of the diameter and radius.
we have that
The circle has a diameter with end points: (4 + 6i) and (-2 + 6i)
we know that
The distance between the end points is equal to the diameter
the formula to calculate the distance between two points is equal to
(4 + 6i) ----> (4,6)
(-2 + 6i) ---> (-2,6)
substitute the values
therefore
The diameter is
The radius is equal to
---> the radius is half the diameter
Part 2) Show me how you would determine the center of the circle
we know that
The center of the circle is equal to the midpoint between the endpoints of the diameter
The circle has a diameter with end points: (4 + 6i) and (-2 + 6i)
The formula to calculate the midpoint between two points is equal to
substitute
therefore
(1,6) ----> (1+6i)
The center of the circle is (1+6i)
Part 3) Determine, mathematically, if (1+9i) lies on the circle. Show how you proved it mathematically
Find the equation of the circle
we have
The center is (1+6i) -----> (1,6)
r=3 units
substitute
Verify if the point (1+9i) lies on the circle
Remember that
If a point lies on the circle, then the point must satisfy the equation of the circle
Substitute the value of x and the value of y in the equation and then compare the results
we have
the point (1+9i) -----> (1,9)
therefore
The point (1+9i) lies on the circle
Part 4) Determine, mathematically, if (2-i) lies on the circle. Show how you proved it mathematically
The equation of the circle is equal to
Verify if the point (2-i) lies on the circle
Remember that
If a point lies on the circle, then the point must satisfy the equation of the circle
Substitute the value of x and the value of y in the equation and then compare the results
we have
the point (2-i) -----> (2,-1)
therefore
The point (2-i) does not lies on the circle