If one endpoint of a diameter of the circle is (-2,-7), what are the coordinates of the other endpoint of this diameter?

Question

In the xy-plne, the center of a circle has coordinates (3,-7). That is the first part of the question.

 

I got the distance and then added it to (-2,-7), but it was incorrect. Please help. Thank you.

Answer 1

The center of a circle on a coordinate plane is located at the point (2, –5). One endpoint of the diameter is located at (6, –7). What are the coordinates of the other endpoint of the diameter of the circle

Answer 2

Hey Anna,

 

With this problem, it would be ideal to use the midpoint formula to find the coordinates of the other endpoint. 

 

The midpoint M has coordinates ( [(x₁+x₂)/2] , [(y₁+y₂)/2] ).

 

In this case, we know that the center of the circle is the midpoint, so:

 

(x₁+x₂)/2 = 3

and

(y₁+y₂)/2 = -7

 

We also know the coordinates of one of the points, so:

 

(-2+x₂)/2 = 3
and
(-7+y₂)/2 = -7

 

From here, we solve for x₂ and y₂, so:

 

(-2+x₂)/2 = 3

-2+x₂ = 6

x₂ = 8
and
(-7+y₂)/2 = -7

-7+y₂ = -14

y₂ = -7

 

Therefore, the coordinates of the other endpoint of the diameter are (8, -7).