Answer:
The coordinates for the location of the center of the platform are (0, 1)
Step-by-step explanation:
The equation of the circle of center (h , k) and radius r is:
(x - h)² + (y - k)² = r²
Now,
- The center is equidistant from any point lies on the circumference of the circle
- There are three points equidistant from the center of the circle
- We have three unknowns in the equation of the circle h , k , r
Thus, let's substitute the coordinates of these point in the equation of the circle to find h , k , r.
The equation of the circle is (x - h)² + (y - k)² = r²
∵ Points A(2,−3), B(4,3), and C(−2,5)
- Substitute the values of x and y the coordinates of these points
Point A (2 , -3)
(2 - h)² + (-3 - k)² = r² - - - (1)
Point B (4 , 3)
(4 - h)² + (3 - k)² = r² - - - - (2)
Point C (-2 , 5)
(-2 - h)² + (5 - k)² = r² - - - - (3)
- To find h , k equate equation (1) and (2) and same for equation (2) and (3) because all of them equal r²
Thus;
(2 - h)² + (-3 - k)² = (4 - h)² + (3 - k)² - - - - - (4)
(4 - h)² + (3 - k)² = (-2 - h)² + (5 - k)² - - - - -(5)
- Simplify (5);
h² - 8h + 16 + k² - 6k + 9 = h² + 4h + 4 + k² - 10k + 25
h² and k² will cancel out to give;
-8h - 6k + 25 = 4h - 10k + 29
Rearranging, we have;
12h - 4k = -4 - - - - (6)
Similarly, for equation 4;
(2 - h)² + (-3 - k)² = (4 - h)² + (3 - k)²
h² - 4h + 4 + k² + 6k + 9 = h² - 8h + 16 + k² - 6k + 9
h², k² and 9 will cancel out to give;
4 - 4h + 6k = 16 - 8h - 6k
Rearranging;
4h + 12k = 12 - - - - (7)
Divide by 4 to give;
h + 3k = 3
Making h the subject;
h = 3 - 3k
Put 3 - 3k for h in eq 6;
12(3 - 3k) - 4k = -4
36 - 36k - 4k = -4
40k = 40
k = 40/40
k = 1
h = 3 - 3(1)
h = 0
The coordinates for the location of the center of the platform are (0, 1)
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