Pqrs is a parallelogram. given that three of the vertices are p(6,-2,4), q(2,4,-8), and r(-2,2,4), determine the coordinates of vertex s.

the vertex and vertices are the same thing but i do not know how to find the fourth point using the distance formula. can someone me?

  S = (2, -4, 16)

Step-by-step explanation:

You don't need the distance formula to find the fourth vertex. The midpoint of the diagonals is the same for both diagonals, so ...

  (P+R)/2 = (Q+S)/2 . . . . midpoints are the same

  P + R = Q + S . . . . . . . .multiply by 2

  P + R - Q = S . . . . . . . .subtract Q to get an equation for S

S = (6, -2, 4) +(-2, 2, 4) -(2, 4, -8)

  = (6 -2 -2, -2 +2 -4, 4 +4 +8)

S = (2, -4, 16)

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.

the answer is c)8

step-by-step explanaction: