Question

Given that the points (-3, 2) and (1, 2) are vertices of a rectangle, what two sets of coordinates could form the other two vertices?
A) (-3, 5) and (2, 5)
B) (-3, 5) and (1, 5)
C) (1, 5) and (2, 5)
D) (-3, 5) and (-1, 5)

Answer 1

The answer is B, -3,5 and 1,5

Answer 2

We could simply plot the other sets of points and find out which set forms a rectangle with the two given points, (-3,2), and (1,2).

However, that seems either too difficult or too easy, such that no one offered a solution that way.  I will still leave that option open for anyone who wishes to try it.

The problem is very much suited for a solution by look at the numbers, in other words, by inspection.

The given (fixed) points are (-3,2) and (1,2), they both lie on the horizontal line y=2.  From the properties of a rectangle, the other two points must be parallel, hence they should also lie on a horizontal line.

Looking at the 4 possible options, we notice that all options have the points lie on the horizontal line y=5, evidenced by the fact that all points have a y-coordinate of y=5.

Thus our only job is to find points such that they line up vertically with the two given points (-3,2), (1,2).  In other words, the other two points must have the coordinates (-3, 5), (1,5) which match the x-coordinates of the given points.

So the above is the method by inspection which can be applied given the two given points lie on a horizontal (or vertical) line.