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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)

Given that the points (-3, 2) and (1, 2) are vertices of a rectangle, what two sets-example-1

2 Answers

4 votes
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.
User Sinead
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1 vote
the answer is B, -3,5 and 1,5
User Prayagupadhyay
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