Question

Verify that quadrilateral BCDE is a rhombus with vertices B(5, -1), C(-2, 0), D( -1, 7) and E(6, 6) by showing that all four sides are equal.

Answer 1

BCDE has the sides: BC, CD, DE, ED

you need to show that all 4 sides are equal in length

Answer 2

to find the length of any segment, you use the distance formula

example: to find the length of BC, you find the distance from point B to point C

Answer 3

the distance formula is

\[\Large d = \sqrt{\left(x_{2}-x_{1}\right)^2+\left(y_{2}-y_{1}\right)^2}\]

Answer 4

I'm trying and i just can't get it

Answer 5

Let's make B the point (x1,y1) and C the point (x2,y2)

Answer 6

B = (x1,y1) = (5, -1)
C = (x2,y2) = (-2,0)

Answer 7

plug the values into the distance formula to get
\[\Large d = \sqrt{\left(x_{2}-x_{1}\right)^2+\left(y_{2}-y_{1}\right)^2}\]
\[\Large d = \sqrt{\left(-2-5\right)^2+\left(0-(-1)\right)^2}\]
\[\Large d = \sqrt{\left(-7\right)^2+\left(1\right)^2}\]
\[\Large d = \sqrt{49+1}\]
I'll let you finish

Answer 8

thank you!!!!

Answer 9

sure thing