Provide an appropriate response.
-Are the points A(0, 3), B(3, 6), C( 5, -2), and D(8, 1) the vertices of a parallelogram (opposite sides equal in length)? of a rhombus (all sides equal in length)?
A) no; no
B) no; yes
C) yes; yes
D) yes; no

Question

Quizplus · Accepted Answer

To determine if these points form a parallelogram, and potentially a rhombus, we calculate the distances between consecutive points (sides) and the diagonals. For a parallelogram, opposite sides must be equal in length, and for a rhombus, all sides must be equal.- AB = sqrt((3-0)^2 + (6-3)^2) = sqrt(9 + 9) = sqrt(18)- BC = sqrt((5-3)^2 + (-2-6)^2) = sqrt(4 + 64) = sqrt(68)- CD = sqrt((8-5)^2 + (1+2)^2) = sqrt(9 + 9) = sqrt(18)- DA = sqrt((8-0)^2 + (1-3)^2) = sqrt(64 + 4) = sqrt(68)AB = CD and BC = DA, so the sides form a parallelogram. However, the lengths of AB and BC (also CD and DA) are not equal, indicating it is not a rhombus.

Provide an Appropriate Response