Question

Show that (-3, 2), (-5, -5), (2, -3) and
(4, 4) are the vertices of a rhombus.​

Answer 1

Answer:

let a(-3,2), b(-5,-5), c(2,-3) and d(4,4) are the vertices

dist ab = √((-5-2)^2 + (-5+3)^2) = √53

similarly calculate bc, cd and da

bc = cd =da = √53

all sides are equal.

slope of diagonal ac = (-3-2)/(2+3)= -1

slope of diagonal bd = (4+5)/(4+5)= 1

since the product of the slope of two diagonal s is 1×(-1) = -1 so two diagonals are perpendicular to each other. So abcd is a rhombus.

Answer 2

Answer:

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