Question

Show that the points (1,7),(4,2),(-1,-1)and (-4,4) are the vertices of a rhombus solve answer in photo

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Answer 1

Step-by-step explanation:

here is your answer please mark it brainliest

Answer 2

Step-by-step explanation:

you can draw a rhomboid with above vertices

we will use property of rhomboid to prove this

property 1. diagonals of rhomboid bisect each other

property 2. diagonals are perpendicular to each other

first of all we will assume that cordinate of vertices have been given in cyclic order i.e. coordinates (1,7) and (-1,-1) are end points of a diagonal (say AC) and coordinated (4,2) and (-4,4) are end points of other diagonal (say BD)

now cordinate of mid point of AC = ((1+-1)/2, (7+-1)/2)

= (0,3)

cordinate of mid point of BD = ((4+-4)/2, (4+2)/2)

= (0,3)

clearly, mid points of the diagonals coincide. i.e. diagonals bisect each other.

now, slope of AC = M1 = (7-(-1))/1-(-1))

= 8/2 = 4

slope of BD = M2 = (4-2)/(-4-4)

= 2/(-8)

= 1/(-4)

now,

M1*M2 = 4*1/(-4) = -1

M1M2 = -1

this proves that the diagonals are perpendicular to each other

This, the diagonals are perpendicular bisectors of each other.

Note: this is possible in case of rhombous and square. however, in order to check whether it is a square, we need to find product of slopes of adjacent sides. However, this is not required as we had to prove it only rhombous which is proved.