Question

The side RS of a quadrilateral PQRS is drawn on a grid as shown.
If quadrilateral PQRS is a square, which of these ordered pair could be a vertex?

(4,-1)
(4,0)
(5,-1)
(5,0)

Answer 1

If we look at the figure, we see that there was a change of 4 in the x dimension and 3 in the y dimension between points S and R. Since the figure is a square, the other sides touching points S and R need to be at a 90 degree angle to the side given and the same length, so they are going to change the same amount but in the opposite dimensions. In other words, points P and Q must be 4 away in the y dimension and 3 in the x from points R and S.

You can choose whether to move up or down in the y dimension; once you do, you need to move in the right direction in the x dimension to make a 90 degree angle. Hence we can go down and right or up and left. Thus, there are 4 possible places points P and Q can be, located at the locations of points R and S + (4, -3) and + (-4, 3)

Then there can be vertices at:
(4+4, 7-3) = (8, 4)
(4-4, 7+3) = (0, 10)
(8+4, -4-3) = (12, -7)
(8-4, -4+3) = (4,-1)

Answer 2

try (0, -4) and (4, -1)

Answer 3

@Bubblez_12 , I guess you didn't like my graphing idea.

Answer 4

i didnt have a graph pare im sorry but i really do appreciate you guys helping me <3

Answer 5

Doing this without graph paper probably isn't a good idea.

Answer 6

Especially the other question