# Distance between Points

The concept of distance between points serves as a fundamental principle in various fields, including mathematics, physics, and geography. It represents the measure of separation between two distinct locations in space, providing a quantitative understanding of spatial relationships. Whether calculating the distance between two cities on a map or determining the length of a vector in a mathematical equation, the concept of distance serves as a cornerstone for analyzing and interpreting spatial data. Understanding the nuances of distance measurement enables individuals to navigate physical and abstract spaces with precision and accuracy, facilitating problem-solving and decision-making processes.

- Circle A has a center at #(3 ,2 )# and a radius of #1 #. Circle B has a center at #(1 ,3 )# and a radius of #4 #. Do the circles overlap? If not, what is the smallest distance between them?
- An isosceles triangle has sides A, B, and C with sides B and C being equal in length. If side A goes from #(7 ,3 )# to #(8 ,9 )# and the triangle's area is #45 #, what are the possible coordinates of the triangle's third corner?
- Circle A has a center at #(2 ,9 )# and an area of #16 pi#. Circle B has a center at #(3 ,8 )# and an area of #67 pi#. Do the circles overlap?
- Using the midpoint formula, if you're only given #((x_1 + x_2) / 2#, #(y_1 + y_2) / 2)#, is it possible to solve for #x# and #y#?
- A triangle has corners at #(1 ,3 )#, #(9 ,2 )#, and #(6 ,7 )#. How far is the triangle's centroid from the origin?
- What is the perimeter of a triangle with corners at #(3 ,8)#, #(1 ,5 )#, and #(4 ,3 )#?
- Circle A has a center at #(1 ,2 )# and an area of #100 pi#. Circle B has a center at #(7 ,9 )# and an area of #36 pi#. Do the circles overlap? If not, what is the shortest distance between them?
- Proof of the shortest distance from a point to a plane formula?
- Circle A has a center at #(2 ,3 )# and an area of #8 pi#. Circle B has a center at #(7 ,2 )# and an area of #64 pi#. Do the circles overlap?
- A triangle has corners at #(2 ,4 )#, #(8 ,6 )#, and #(7 ,9 )#. How far is the triangle's centroid from the origin?
- Circle A has a center at #(2 ,3 )# and a radius of #5 #. Circle B has a center at #(3 ,8 )# and a radius of #1 #. Do the circles overlap? If not what is the smallest distance between them?
- Circle A has a center at #(6 ,2 )# and an area of #45 pi#. Circle B has a center at #(2 ,3 )# and an area of #75 pi#. Do the circles overlap?
- Circle A has a center at #(3 ,7 )# and an area of #56 pi#. Circle B has a center at #(9 ,6 )# and an area of #28 pi#. Do the circles overlap?
- Circle A has a center at #(9 ,-2 )# and a radius of #1 #. Circle B has a center at #(1 ,3 )# and a radius of #3 #. Do the circles overlap? If not, what is the smallest distance between them?
- What is the perimeter of a triangle with corners at #(7 ,5 )#, #(1 ,2 )#, and #(4 ,8 )#?
- Triangle ABC is graphed on a coordinate plane. find the length of AB?
- What is the approximate distance between points (-7,2) and (11, -5)?
- Circle A has a center at #(2 ,7 )# and an area of #81 pi#. Circle B has a center at #(4 ,3 )# and an area of #36 pi#. Do the circles overlap? If not, what is the shortest distance between them?
- A triangle has corners at #(4 ,1 )#, #(8 ,3 )#, and #(3 ,5 )#. How far is the triangle's centroid from the origin?
- An isosceles triangle has sides A, B, and C with sides B and C being equal in length. If side A goes from #(1 ,4 )# to #(5 ,1 )# and the triangle's area is #15 #, what are the possible coordinates of the triangle's third corner?