Given:
Two endpoints of a diameter of a circle:
P (-7, -10)
Q (3, 2)
a) To find the center of the circle, find the midpoint of the two points:
midpoint:
(x2 - x1 )/ 2 , (y2 - y1) / 2
x= (2 - (-7))/2 = 4.5
y= (3 - (-10))/2 = 6.5
Therefore, the center of the circle is at C(4.5, 6.5)
b) To find the radius of the circle, we need to find the distance between the two points and divide by 2.
d = √(y2-y1)^2 + (x2 - x1)^2
d = √(2-(-7))^2 + (3 - (-10))^2
d = 5√10 = diameter
r = d/2 = 5√10 /2
Step-by-step explanation:
8√383 by √3√333.
8√3⋅√3√383⋅33
Combine and simplify the denominator.
Tap for more steps...
8√33833
The result can be shown in multiple forms.
Exact Form:
8√33833
Decimal Form:
4.61880215
<span>the value under the square root i.e. b²-4ac is called Discriminant (D) and its value tells us about the nature of the roots of the equation. If D = 0, the roots are real & equal if D > 0, the roots are real & different if D< 0, the roots are imaginary & different</span>
Slope formula:
m = y2 - y1 / x2 - x1
Line QR: (2,8) (3,10)
m = 10 - 8 / 3 - 2 = 2 / 1 = 2
Line ST: (0,6) (-2,2)
m = 2 - 6 / -2 - 0 = -4/-2 = 2
<span>c. parallel because the slopes are the same</span>