Question

A square has a perimeter of 12 units. One vertex is at the point (-1,1), and another vertex is at the vertex (2,4) which of the following could be another vertex?
(1,2)
(2,1)
(1,-2)
(2,-1)

Answer 1

The formula for the perimeter of a square is P=4a where "P" is the perimeter and "a" is for the length of the side. In this problem, the perimeter is given which is equal to 12 units, then we can solve for the distance or length of the side which is shown below:
P=4a
12=4a
a=3 units 

The answer is (2,1) and  proof of this is the distance should be equal to 3 units
at the vertex (2,4)
d²=(2-2)²+(4-1)²
d²=0²+3²
d=3 units

Hence, answer is (2,1)
 

Answer 2

This could be a lot easier if you use a graphing paper and plot the given points (-1,1) and (2,4). Forming a square, you will derive with the points (-1,4) and (2,1) which is in the choices. So if you don't know the formula or don't know how to solve this through calculation, use a graphing paper. The answer is (2,1).