Question

The endpoints of one diagonal of a rhombus are (-5, 2) and (1, 6). If the coordinates of the 3rd vertex are (-6, 10), what are the coordinates of the 4th vertex?

Answer 1

Answer:(2,-2)

Explanation:

Answer 2

Explanation:

The endpoints of one diagonal of a rhombus are (-5, 2) and (1, 6). The coordinates of the 3rd vertex are (-6, 10), the fourth vertex we have to find out

Since diagonals of a rhombus bisect each other the midpoints of the two diagonals would be the same

Let A be (-5,2) andC be (1,6)

If E is the mid point of AC, then coordinates of E

=
`((-5+1)/(2) ,(2+6)/(2) )\\=(-2,4)`

E is also midpoint of other vertices Band D

Let B be (-6,10) and D be (x,y)

Midpoint of BD =

`((x-6)/(2) ,(y+10)/(2) )=(-2,4)`

x=2 and y =-2