Quadrilateral ABCD has coordinates A (3, 5), B (5, 2), C (8, 4), D (6, 7). Quadrilateral ABCD is a (4 points)
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Answer: To find the equation of the circle, it is not necessary to find the legs of the triangle first.
The length of the legs (equal) is 3√2 or 4.243
Step-by-step explanation:
The equation for a circle is similar to the Pythagorean Theorem
a² + b² = c²
( x - h )² + ( y - k )² = r², where ( h, k ) is the center and r is the radius.
The a and b terms are changed to allow insertion of h and k to locate the center of the circle on a Cartesian plane.
You can get the information needed from
Given: radius =6 and "a center at the point (3,2)"
Substitute 3 for h and 2 for k and 6 for r
( x - 3 )² + ( y - 2 )² = 6² This is the equation of the circle .
From the diagram, it appears that x-3 = y-2
So, in the equation, we can substitute 2(x²) = 36
x² = 36/2 . x² = 18
√x² = √18 = √9(2)
x = 3√2 =4.2426
the length of the horizontal leg is 4.243
Substitute for x in to find x+3 the coordinate (x,2)
the coordinate x, 2 is (7.24, 2)
Substitute for y in to find y+2, the length of the vertical leg is 4.243.
y + 2 = 6.243
So the coordinate (x,y) on the circle is (7.24, 6.24)
This does not account for Step 1 and Step 2 in the question, matching expressions or equations to the steps. I hope you will be able to sort that our with the information here.
