Consider a shape with vertices A (1, 4), B (3, 0), C (1, - 4), and D (-1, 0) on the coordinate plane. 1) Which proves that the shape given by the vertices is a rhombus? A) AB = BC = CD = DA = 10 B) AB = BC = CD = DA = 15 C) AB = BC = CD = DA = 2 5 D) AB = BC = CD = DA = 3 5

C) AB = BC = CD = DA = 2√5

Corrected question:

Consider a shape with vertices A (1, 4), B (3, 0), C (1, - 4), and D (-1, 0) on the coordinate plane. 1) Which proves that the shape given by the vertices is a rhombus? A) AB = BC = CD = DA = 10 B) AB = BC = CD = DA = 15 C) AB = BC = CD = DA = 2√5 D) AB = BC = CD = DA = 3√5

Step-by-step explanation:

Given;

Vertices

A (1,4)

B (3,0)

C (1,-4)

D (-1,0)

We need to determine the Length of sides;

AB, BC, CD, DA

Length = √ ((∆x) ^2 + (∆y) ^2)

For

AB = √ ((3-1) ^2 + (0-4) ^2) = √ (4+16) = √20 = 2√5

BC = √ ((1-3) ^2 + (-4-0) ^2) = √ (4+16) = √20 = 2√5

CD = √ ((-1-1) ^2 + (0--4) ^2) = √ (4+16) = √20 = 2√5

DA = √ ((1--1) ^2 + (4-0) ^2) = √ (4+16) = √20 = 2√5

Which shows that;

AB=BC=CD=DA=2√5

For a rhombus, all sides are equal.

Therefore, AB=BC=CD=DA=2√5, proves that the shape given by the vertices is a rhombus.