A square with area 25 has one vertex on point (-2, 1) in the coordinat

Question

A square with area 25 has one vertex on point (-2, 1) in the coordinate plane. From the table below, select the x- and y-coordinates that could correspond to another vertex of this same square.

Sajjad1994 · Answer

Official Explanation

(-5, -3) is the only point that will work. From the answer choices you should see that the only available options are in Quadrant III, so that should help you to limit your search. You must go down on the y-coordinate and the only way to go to the right on the x is to go to -1. But since the sides of the square are equal to 5, you're looking for a point 5 spaces away from (-2, 1). That means that x = -7 is in play, but then you'd have three options for y: staying at 1 (not an option), moving up to 6 (not an option) or going down to -4 (also not an option). So your only choice here is to recognize another way to move exactly 5 spaces - keeping all values integers - in the coordinate plane: the 3-4-5 triangle. If you were to move 3 spaces left (to x = -5) and 4 spaces down (to -3), that is a point exactly 5 spaces away from the initial vertex, allowing point (-5, -3) to be another vertex.

Answer: (-5, -3)

ArjunKumar25 · Answer

I really think the answer is wrong. I tried plotting this graph on desmos and its not possible for it be a square with these coordinates

as.hish404 · Answer

YESS.....ans should be (-7,-4) or (-2,-4) or the area of the sq. should be 16 not 25.

bb · Answer

This is a strange question... an evil one maybe? I also assumed that the square was going to be located straight on and there were 4 options.
Instead, it seems the question assumes that the distance between (-2, 1) is more like a center of a circle and then another vertex can be 5 units away in any direction.

I have drawn 2 squares - a blue one (correct answer)
And a yellow one which is the exact same square (I copied it and pasted it but then removed the tilt without changing the size), so it is possible but it is not pretty. 
P.S. Thank you  ArjunKumar25  for the useful tool. Made it in desmos

https://gmatclub.com/blog/wp-content/uploads/2024/01/square2.webp

chetan2u · Answer

There could be two ways the square could be made.

1) Sides parallel to x and y axis
The coordinates then should be such that one of the two remains constant and other increases/decreases by 5. For example (-2+5,1) or (3,1), (-7,1), (-2,6), (-2,-4). It could also be diagonally opposite vertex but then it will not be integers. Nothing in option.

2) Sides slanting to x and y axis 
Now, the side will become a hypotenuse. So hypotenuse is 5, as the side is 5. 
The triangle made by this hypotenuse could have sides in ratio 3:4:5.
Now x could be 3 or 4. => If it were 4, -2-x=4 or x-2=4 would require x to be even. But the options are all odd. 
So x should become 3 using one of the options. -2-x=5 or x=-7.
Also y can become 4 from given options. 1-y=4 or y=-3.

See the attached figure for reference.

reyrest · Answer

evil is the right word.. how do we calculate the co-ordinates when the square is of this form?

charlie1195 · Answer

Hello!
I solved this question using the distance formula. 
We know that the side of the square is 5 units, since side = sqrt (area) = sqrt (25) = 5

Let the coordinates of the vertex we want to find be (x,y). We know the already existing coordinates are (-2, 1)
Now, Using the distance formula, 
sqrt( (x - (-2))^2 + (y-1)^2 ) = 5
Squaring both side, 
(x+2)^2 + (y-1)^2 = 25

Now among the options, we can completely discard -7 and -9 since the LHS will become more than 25 in both the cases. 
We are left with -1, -3 and -5. 
We also know that 25 = 3^2 + 4^2
So, x+2 is equal to either 3 or -3, or 4 or -4
From the options, only x+2 = -3 is the feasible option
Hence, x = -5
Similarly, y-1 is equal to either 4 or -4
From the options, we see -3 is fulfiling this criteria. 
Hence, y = -3

Hope this helps

A square with area 25 has one vertex on point (-2, 1) in the coordinat

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x-coordinate	y-coordinate	---------------
		-9
		-7
		-5
		-3
		-1

GMAT Two-part Analysis (TPA) Questions

A square with area 25 has one vertex on point (-2, 1) in the coordinat

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