How do I solve this without graphing the points? Verify that quadrilateral BCDE is a rhombus with vertices B(-5, 1), C(0, 6), D(5, 1) and E (0, -4) by showing that all four sides are equal.

Question

anonymous · Answer

@ganeshie8 or @ikram002p

campbell_st · Answer

use the diagonals... use the distance formula to show there are not equal in length

then find the gradients of the diagonals and show they intersect at right angles... 

then you can prove its a rhombus

campbell_st · Answer

oops replace gradient with slope

anonymous · Answer

What is the distance formula? Sorry I forgot it.

campbell_st · Answer

the distance formula is 

$$d = \sqrt{x_{2} -x_{1})^2 + (y_{2} - y_{1})^2}$$

where you have 2 points 

$$(x_{1}, y_{1}) ..and...(x_{2}, y_{2})$$

anonymous · Answer

Oh yeah. Ok I'm gonna do that real quick.

campbell_st · Answer

opps... you need to show the 4 sides are equal... I just re-read the question... 

so the distance formula for the sides

BC, CD, DE, EB

sorry about that

anonymous · Answer

Ok thanks.