Lesson: The Coordinate Plane

Comment on The Coordinate Plane

P,Q, and R are three points in a plane, and R does not lie on line PQ. Which of the following is true about the set of all points in the plane that are the same distance from all three points?
A) it contains no points
B) it contains one point
C) it contains two points
D) it is a line
E) it is a circle

Brent, how to tackle these kind of question faster. I assumed points under a equilateral triangle and I thought midpoint of triangle is only point which is possible to be at equidistant from all three given points. So answer was B. Somehow correct answer given was also B.
greenlight-admin's picture

Hi yogasuhas,

This is VERY high-level question. You can find my detailed response here: http://greprepclub.com/forum/topic1885.html#p9785

https://greprepclub.com/forum/qotd-9-in-the-xy-plane-a-quadrilateral-has-vertices-2498.html
In the vertical planes (-1,4) (-1,-5) why can't we subtract -1-(-1) why just 4-(-5)
greenlight-admin's picture

Question link: https://greprepclub.com/forum/qotd-9-in-the-xy-plane-a-quadrilateral-has...

I assume you're wanting to apply the formula for finding distances between points (as is taught at 1:40 of the following video: https://www.greenlighttestprep.com/module/gre-algebra-and-equation-solvi...

When we plug the two x-coordinates (-1 and -1) into the formula, we get (-1) - (-1) = 0
Since the difference is 0, those values have no effect on the distance, so we can ignore them.

Alternatively, we can also recognize that if two points are an the same vertical line, we need only examine the y-coordinates.

For example, if we sketch the points (0,1) and (0,5) on the x-y plane, we can quickly see that the distance between the points is 4 (since 5 - 1 = 4)

However, if we want to apply the distance formula, we'll still get 4 (except it will take a little longer that way :-)

Does that help?

Cheers,
Brent

https://greprepclub.com/forum/gre-math-challenge-118-coordinate-geometry-776.html
Doesn't triangle ORS have a height of -1
greenlight-admin's picture

Question link: https://greprepclub.com/forum/gre-math-challenge-118-coordinate-geometry...

Distances and heights are only measured in positive values. So, the height must be 1.

Cheers,
Brent

https://greprepclub.com/forum/qotd-9-in-the-xy-plane-a-quadrilateral-has-vertices-2498.html

please expound this question.
greenlight-admin's picture

Question link: https://greprepclub.com/forum/qotd-9-in-the-xy-plane-a-quadrilateral-has...

One way to determine the length of each side is to apply some logic/number sense (as Sandy has done in his linked solution).

HOWEVER, another approach is the apply the distance formula, which is covered here: https://www.greenlighttestprep.com/module/gre-algebra-and-equation-solvi...

So, for example, to determine the distance from (-1, 4) to (7, 4), we can plug the coordinates into the distance formula.

We get: distance = √[(7 - -1)² + (4 - 4)²]
= √[8² + 0²]
= √[8²]
= 8
We can use the same process for the other sides as well.

Does that help?

Cheers,
Brent

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