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Parallelogram OPQR lies in the xy-plane [#permalink]
27 Dec 2015, 19:42

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Question Stats:

78% (01:48) correct
21% (01:54) wrong based on 23 sessions

Parallelogram OPQR lies in the xy-plane, as shown in the figure above. The coordinates of point P are (2, 4) and the coordinates of point Q are (8, 6). What are the coordinates of point R ?

A. (3, 2) B. (3, 3) C. (4, 4) D. (5, 2) E. (6, 2)

Practice Questions Question: 10 Page: 158 Difficulty: hard

Re: Parallelogram OPQR lies in the xy-plane [#permalink]
27 Apr 2016, 08:27

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It is a parallelogram. If the distance between O to P in “X”axis is 2, the distance between R to Q in “X” axis must be 2. So, Distance between O to R in “X” axis will be 8-2= 6. Similarly, If the distance between O to P in “Y”axis is 4, the distance between Q to R in “Y” axis must be 4. So, Distance between O to R in “Y” axis will be 6-4= 2. The point at R= (6,2)

Re: Parallelogram OPQR lies in the xy-plane [#permalink]
15 Sep 2017, 00:14

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I have used the fact that PQ and OR must be parallel since the figure is a parallelogram, then the slope of PQ must be the same as OR. The slope of PQ is equal to 1/3, thus, given that O=(0,0), R must be equal to (6,2) in order to have a slope of 1/3, i.e. (2-0)/(6-0) = 1/3.

Re: Parallelogram OPQR lies in the xy-plane [#permalink]
20 Mar 2018, 13:27

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Expert's post

sandy wrote:

Parallelogram OPQR lies in the xy-plane, as shown in the figure above. The coordinates of point P are (2, 4) and the coordinates of point Q are (8, 6). What are the coordinates of point R ?

A. (3, 2) B. (3, 3) C. (4, 4) D. (5, 2) E. (6, 2)

KEY CONCEPT: Since OPQR is a parallelogram, we know that sides PQ and OR are parallel AND the same length

Let's take a closer look at side PQ

Notice that, to get from point P to point Q we must move 2 units UP and move 6 units RIGHT.

Since sides PQ and OR are parallel AND the same length, the same must apply to points O and R So, if we start from point O (at 0,0) and move 2 units UP and move 6 units RIGHT, we must get to point R

From here, it we can determine the coordinates of point R

Answer: E

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Re: Parallelogram OPQR lies in the xy-plane [#permalink]
27 Jun 2018, 20:47

The slope of the line from the origin to point P is the same as the slope of the line from point Q to R because we have a parallelgram. The same is true for the lines between points P and Q and the origin and point R. The slope of the line from the origin to P is 2, so it follows that the slope of the line between between Q and R is also 2. Now we can determine the equations of the lines between the origin and R and also between Q and R. Given points P and Q, it is easy to see that the slope line between these points is 1/3. It follows that the slope of the line between the origin and R is also 1/3. Hence, the equation of the line from the origin to R is y=1/3X. Using the fact that the slope of the line between Q and R is 2 and we are given that the coordinates of Q are (8,6), we can determine the equation of the line between Q and R to be Y=2X-10 using the point-slope method. We can determine the coordinates of R by setting the equations of the lines Y=1/3X and Y=2X-10 together. Solve for X: 1/3X=2X-10, So X is 6. Plug 6 into Y=1/3X or Y=2X-10 to get Y=2. Answer: (6,2).

greprepclubot

Re: Parallelogram OPQR lies in the xy-plane
[#permalink]
27 Jun 2018, 20:47