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

Question

Quizplus · Accepted Answer

To determine if these points form a parallelogram or a rhombus, we can calculate the distances between consecutive points (sides of the shape) and check for the conditions of each figure. For a parallelogram, opposite sides must be equal in length. For a rhombus, all sides must be equal in length.- Distance AB = sqrt[(0 - (-3))^2 + (6 - 5)^2] = sqrt[9 + 1] = sqrt[10]- Distance BC = sqrt[(2 - 0)^2 + (-2 - 6)^2] = sqrt[4 + 64] = sqrt[68]- Distance CD = sqrt[(5 - 2)^2 + (1 - (-2))^2] = sqrt[9 + 9] = sqrt[18]- Distance DA = sqrt[(-3 - 5)^2 + (5 - 1)^2] = sqrt[64 + 16] = sqrt[80]Since none of the distances are equal, the points do not form a parallelogram (opposite sides are not equal) nor a rhombus (all sides are not equal).

Provide an Appropriate Response