what would be the answer cause it makes no sense to me
Find the radius of Circle P if its endpoints are (-4, 3) and (2, -1).
along with this one
In a circle, a minor arc = 20x + 15 and the major arc = 30x + 45. Find the length of the major arc.
I guess by endpoints they mean opposite ends of a diameter
so
the radius is half the distance between the two points
range in x = 2 + 4 = 6
range in y = 3 + 1 = 4
diameter^2 = 16 + 36 = 52
so diameter = sqrt 52 = 7.21
and radius = 3.6
The sum of the major arc and the minore arc is the circumference 2 pi R or pi D
so
20 x+15 + 30 x + 45 = pi D
50 x + 60 = pi D
That is all I can say without knowing D or R
To find the radius of a circle given its endpoints, you can use the distance formula.
The distance formula is √((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the coordinates of the endpoints.
Let's apply this formula to the first question:
Given endpoints: (-4, 3) and (2, -1)
Using the distance formula, the radius of the circle can be found as follows:
Step 1: Calculate the difference between the x-coordinates: 2 - (-4) = 6
Step 2: Calculate the difference between the y-coordinates: -1 - 3 = -4
Step 3: Square each difference: 6^2 = 36 and (-4)^2 = 16
Step 4: Add the squared differences: 36 + 16 = 52
Step 5: Take the square root of the sum: √52 = 2√13
Therefore, the radius of Circle P is 2√13.
Now let's move on to the second question:
To find the length of the major arc, we need to know the measure of the central angle of the major arc.
The measure of a central angle is equal to the ratio of the arc length to the circumference of the circle it corresponds to.
The circumference of a circle is given by the formula 2πr, where r is the radius.
In this case, the major arc is represented by the expression 30x + 45.
To find the length of the major arc, we need to know the value of x. However, without additional information, we cannot determine the value of x and therefore cannot calculate the arc length.
Therefore, without knowing the value of x, we cannot find the length of the major arc.