Question

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.

Answer 1

Find the distance between each

between points (x1,y1) and (x2,y2)
D=$\sqrt{(x2-x1)^2+(y2-y1)^2}$



find and verify that
BC=CD=DE=EB

so
BC=$\sqrt{(0-(-5))^2+(6-1)^2}$=5√2
CD=$\sqrt{(5-0)^2+(1-6)^2}$=5√2
DE=$\sqrt{(-4-1)^2+(0-5)^2}$=5√2
EB=$\sqrt{(-5-0)^2+(1-(-4))^2}$=5√2

true