Bob A. answered • 05/09/14

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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 = √ (Δx

^{2}+ Δy^{2})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}= r^{2}so just put the values you know into the equation.

2-

the standard form of an equation in point-slope form is

(y-y

_{1}) = m (x-x_{1}) where m is the slope and (x_{1},y_{1}) is one of the pointsSo find the slope from Δy/Δx

= (y

_{2}-y_{1}) / (x_{2}-x_{1})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 x

_{1}and y_{1}