Question

Rhombus BCDE is shown below. Give the coordinates of C and D.

Answer 1

The coordinates of C - (2n, 0) and the coordinates of D - (n, -p). The diagonals of a rhombus are perpendicular and bisect each other.

What are the properties of a rhombus?

The properties of a rhombus are:

• All the sides of a rhombus are congruent and equal
• Opposite sides are parallel
• Opposite angles are equal
• The adjacent angles add up to 180°
• Diagonals perpendicularly bisect each other
• Diagonals bisect opposite angles

Calculation:

The given rhombus BCDE has B(n, p) and E(0, 0).

Since the diagonals of a rhombus are perpendicular bisectors,

EO = OC or BO = OD

Where O is the midpoint of EC and BD.

In the given diagram, points B and D are opposite each other. They are reflecting each other over the x-axis.

So, if B has coordinates (n, p) then its reflection over the x-axis is (x, -y) i.e., (n, -p).

Thus, we have B(n, p), D(n, -p), and E(0, 0)

Consider the coordinates of C as (x, y).

The midpoint of BD = ($\frac{n+n}{2}$, $\frac{p-p}{2}$)

⇒ coordinates of O = (n, 0)

So,

The midpoint of EC = ($\frac{0+x}{2}$, $\frac{0+y}{2}$)

⇒ coordinates of O = (x/2, y/2)

⇒ (n, 0) = (x/2, y/2)

∴ x = 2n and y = 0

Then, the coordinates of C are (2n, o)

Therefore, the required coordinates of the given rhombus are C(2n, 0) and D(n, -p).

Learn more about the properties of a rhombus here:

https://brainly.com/question/22436329

#SPJ1