Let the coordinates of the circumcentre O of the triangle DEF be (x, y). Circumcentre of a triangle is equidistant from each of the vertices.
1. Distance OD=distance OE, then:
.
2. Distance OD=distance OE, then:
.
Solve the system:
,
,
.
Then
.
Answer: the coordinates of the circumcenter for ∆DEF are x=4.5, y=-1.
The question is incomplete. The complete question is :
Georgia has some 4-inch cubes like the one shown below. Georgia will put the cubes in the box shown below. What is the total number of cubes that Georgia needs to exactly cover the bottom of the box with a layer one cube deep?
Solution :
It is given that :
There are small cubes that has a dimension of 4 in x 4 in x 4 in.
There is also a box which has a dimension of 24 in x 20 in x 12 in.
We need to find out how many small cubes will Georgia need to cover the bottom of the box.
So, we need to find out the surface area of the one cube and the box.
Therefore, the surface area of one cube = side x side
= 4 inch x 4 inch
= 16 square inches
Similarly the area of the box can be find by = length x breath
= 24 in x 20 in
= 480 square inches
Therefore, dividing the area of the box by the area of the cube, we get
= 30
So Georgia will require exactly 30 cubes to cover the bottom of the box with a layer of one cube deep.