Question

Verify that quadrilateral BCDE is a rhombus with vertices B(-5, 1), C(0, -4), D(5, 1) and E (0, 6) by showing that all four sides are equal.

Answer 1

Hi drpick :)

How are you dear?

Answer 2

It is very easy.

Find distances from one point to another and you will find that all distances are equal.

Answer 3

Hence in Rhombus all sides are equal.

Answer 4

Find distances between
BC
CD
DE
EB

Answer 5

Use this formula to find result
\[\Large \sqrt{(y_2-y_1)^2+(x_2-x_1)^2}\]

Answer 6

\[
BC^2=(-4-1)^2+(0+5)^2=50\\
CD^2=(5+0)^2++(1+4)^2=50
\]
Find the square of the other two sides in the same way.