How do I find the endpoint of the diameter if the center is (-3,0) and one endpoint is (4,5)

Question

this is apart of a worksheet called circle terminology

Answer 1

Let (x,y) is second endpoint. Then (x + 4)/2 = - 3 and (y + 5)/2 = 0; from here x = -10 and y = -5.

So 2nd endpoint is (--10, -5)

Answer 2

You can simply do the following.

distancey = |endy - centerx | = ||5 - 0} = 5

distancex = |endx- centerx| = | 4 - (-3)| = 4 + 3 = 7

Then do 0 - 5 = -5

-3 - 7 = -10

The other endpoint will be (-10, -5)

Answer 3

Use Mid-point formula to calculate this since the the relationship between the diameter and radius of a circle is d = 2r ,where d = diameter and r = radius. Therefore, if we use mid-point formula, where x = (x_1 + x_2)/2 and y = (y_1+y_2)/2, where in our case, we have (-3,0) as (x,y), (4,5) as (x_2, y_2) and you need to plug in those values in the mid-point formula equation to get the values of x_1 and y_1. You should get x_1 = -10 and y_1 = -5. Therefore, the other end of the diameter has coordinates (-10,-5).

You can check if I am correct or wrong by finding the distance between (-10,-5) and (-3,0) and between (-3,0) and (4,5) and see if both are equal or not. It will be equal and you should get sqrt(74) in both cases which means that we are correct.