Question

Three vertices of a parallelogram are shown in the figure below.

Give the coordinates of the fourth vertex.
(-5,-3)
(2,7)
(0, -1)

Answer 1

Explanation:

it is a parallelogram.

in comparison to a rectangle one side is shifted a bit, but the endpoints of the shifted side are still positioned the same way relative to each other.

and particularly, their relative offset from each other must be the same as for the endpoints of the other, parallel side.

let's look at

(0, -1) and (2, 7).

their relative offset is given by

x + 2 (from 0 to 2)

y + 8 (from -1 to 7)

the missing point must have the same offset from (-5, -3), as this line is parallel to the one above :

-5 + 2 = -3

-3 + 8 = 5

so, the missing point is (-3, 5).