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

These are my answer choices

A. BD = CD = \[\sqrt{50}\]
B. BD = CE = 50

C.BC = CD = DE = EB = 50

D. BC = CD = DE = EB = \[\sqrt{50}\]

Answer 2

How would you solve this? Please help!

Answer 3

To find the length of each side, you use the distance formula

This works because the distance from B to C is the same as the length of segment BC

Answer 4

Distance formula

\[\LARGE d = \sqrt{\left(x_1 - x_2\right)^2+\left(y_1 -y_2\right)^2}\]

Answer 5

For example

B = (x1,y1) = (5,-1)
so x1 = 5 and y1 = -1

C = (x2,y2) = (-2,0)
so x2 = -2 and y2 = 0


\[\LARGE d = \sqrt{\left(x_1 - x_2\right)^2+\left(y_1 -y_2\right)^2}\]
\[\LARGE d = \sqrt{\left(5 - (-2)\right)^2+\left(-1-0\right)^2}\]
\[\LARGE d = \sqrt{\left(5 +2\right)^2+\left(-1-0\right)^2}\]
\[\LARGE d = \sqrt{\left(7\right)^2+\left(-1\right)^2}\]
\[\LARGE d = \sqrt{49+1}\]
\[\LARGE d = \sqrt{50}\]
\[\LARGE d = \sqrt{25*2}\]
\[\LARGE d = \sqrt{25}*\sqrt{2}\]
\[\LARGE d = 5\sqrt{2}\]

So the exact distance from B to C is \(\Large 5\sqrt{2}\) units

The approximate length of BC (ie the approx distance) is 5*sqrt(2) = 7.0710678

Answer 6

do the same for the other side lengths

Answer 7

Thank you! @jim_thompson5910

Answer 8

you're welcome