. a. Prove that R(­5,0), H(2,­1), O(7,4) and M(0,5) are the vertices of a rhombus. b. Prove that this rhombus is not a square.

Question

. a. Prove that R(­5,0), H(2,­1), O(7,4) and M(0,5) are the vertices of a rhombus.

b. Prove that this rhombus is not a square.

Answer 1

Use the distance formula to compute the lengths of all four sides

sqrt((x2-x1)^2 + (y2-y1)^2), where (x1,y1),(x2,y2) are vertices of each side.

If all four lengths are equal, then the figure is a rhombus

Use the slope formula to compute the slopes of all four sides:

(y2-y1)/(x2-x1).

If the product of the slopes of any of the adjacent sides is not equal to -1 then the figure is not a square