
Bob A. answered 05/09/14
Tutor
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20 Years Making Science and Maths Understandable and Interesting!
1-part a)
make a sketch and you can see that if you make a right triangle with these two points the diameter is the hypotenuse of the triangle with sides Δx and Δy
so use Pythagoras's Theorem to find the diameter
Diameter = √ (Δx2 + Δy2)
you should be able to calculate from here
part b)
the center of the circle will lay on the Diameter 1/2 way between the ends
so the coordinates of the center are (a,b)
where a is 1/2 way between the two x coordinates 7 and 9 => 8
and b is 1/2 way between the two y coordinates -6 and 4 => you can calculate this
part c)
where (a,b) is the center of a circle and r = radius = 1/2 D
the standard form of the equation for a circle is:
(x-a)2 + (y-b)2 = r2
so just put the values you know into the equation.
2-
the standard form of an equation in point-slope form is
(y-y1) = m (x-x1) where m is the slope and (x1,y1) is one of the points
So find the slope from Δy/Δx
= (y2-y1) / (x2-x1)
once you know the slope put that in the standard form for m
and pick one of the points (x,y) to put in the std. form for x1 and y1