1 Find the equation of a sphere if one of the diameters has endpoints A(5,4,3) and B(1,6,-9).
2 Find the equation of a sphere if one of the diameters has endpoints A(5,4,3) and B(1,6,-9).
2 Determine whether the points A(1,0,1), B(2,1,-1), and C(3,2,1) all lie on the same straight line.
3 Determine whether the triangle with corners at A(1,2,3), B(2,4,5) , C(3,6,7) is a) a right triangle b) an isosceles triangle.
4 Find an equation of the set of all points equidistant from the points A(-1,5,3), and B(6,2,-2).
#1. The center is at O=(A+B)/2 = (3,5,6)
For the radius, just find the distance from O to A or B.
#2. same as #1
#3. They all lie on the same line if the slope of AB is the same as the slope of BC
Then check the side lengths, using the distance formula and the Pythagorean Theorem.
#4. Same as #1,2. The center is at (A+B)/2