Respuesta :
Answer:
a) The centre of the circle is the point (-3, 2)
b) the radius of the circle is sqrt(65)
c) the equation of the circle is 65=(x+3)+(y-2)
Step-by-step explanation:
a)
To find the middle point of a segment given its coordinates we apply the following formula:
(x,y)=[(x1-x2)/2; (y1-y2)/2]
Given the coordinates (-10, -2) and (4, 6), let:
x1=-10
x2= 4
y1=-2
y2=6
Applying the formula:
(x,y)=(-10+4)/2; (-2+6)/2
(x,y)=(-6/2); (4/2)
(x,y)=(-3; 2)
b)
To find the radius we can use the distance formula:
where x1 and y1 are the coordinates of point p (one could also use point q) and x2 and y2 are the coordinates of the centre of the circle.
d=sqrt[(x1-x2)^2+(y1-y2)^2]
d=sqrt[(-10+3)^2+(-2-2)^2]
d=sqrt[(-7^2+-4^2]=sqrt[49+16]=sqrt[65]
c)
The equation of a circle is given by the following formula:
(x-x0)+(y-y0)=r^2
where x0 and y0 are the coordinates of the centre of the circle.
In this case:
x0=-3
y0= 2
r^2=65
Therefore, the equation for the circle is:
65=(x+3)+(y-2)
