Question

What are the coordinates of the vertices of the following rhombus centered at the origin, with SW = 2r and TZ = 2t? a) O(2r, 0), W(0, 2t), S(-2r, 0), Z(0, -2t) b) O(2r, 0), Y(0, 2t), S(-2r, 0), T(0, -2t) c) O(2r, 0), T(0, 2t), S(-2r, 0), Y(0, -2t) d) O(2r, 0), Y(0, 2t), W(-2r, 0), T(0, -2t)

Answer 1

The vertices of the rhombus centered at the origin with given dimensions are S(-2r, 0), W(0, 2t), T(0, -2t), and Z(2r, 0).

Step-by-step explanation:

You are asked to determine the coordinates of the vertices of a rhombus that is centered at the origin of a Cartesian coordinate system. The given dimensions of the rhombus are SW = 2r and TZ = 2t. Assuming that S and W lie on the x-axis and T and Z lie on the y-axis, the vertices of the rhombus can be represented as follows:

• S(-2r, 0)
• W(0, 2t)
• O(0, 0) - the center of the rhombus which is at the origin
• T(0, -2t)
• Z(2r, 0)

Therefore, the correct coordinates for the vertices of the rhombus are S(-2r, 0), W(0, 2t), T(0, -2t), and Z(2r, 0).