A square with sides 7 units long is shown below. One corner is the point (5, - 1). Find the other three corners.

Question

Quizplus · Accepted Answer

Since we have one corner at (5, -1), we know that the opposite corner must have the same y-coordinate (since it's a square). This gives us point C as (5, 6). 
To find point B, we can use the distance formula since we know that the length of each side of the square is 7 units. The distance between points (5,-1) and B must be 7 units, so we can set up the equation:
sqrt((5-x)^2+(-1-y)^2)=7
Since B is also on the square, it must be the same distance away from C as it is from (5,-1). This gives us another equation:
sqrt((5-x)^2+(6-y)^2)=7
We can solve this system of equations to find that B is (-2,6).
Finally, to find point A, we can use the fact that it's a square to determine that it must be the same distance away from B as it is from (5,-1). Using the distance formula again, we get:
sqrt((-2-x)^2+(6-y)^2)=sqrt((5-x)^2+(-1-y)^2)
Simplifying this equation gives us -x + y = -3. We also know that A is on the same line as point B and has the same x-coordinate, so we get A = (-2,-1). Therefore, the answer is (A) A=(-2,-1); B=(-2,6); C=(5,6).

A Square with Sides 7 Units Long Is Shown Below