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Math Expert V
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In the figure above, what are the coordinates of point R ?  [#permalink]

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Difficulty:   5% (low)

Question Stats: 80% (01:05) correct 20% (01:04) wrong based on 1237 sessions

### HideShow timer Statistics In the figure above, what are the coordinates of point R ?

A. (3,−5)

B. (3,−3)

C. (5,5)

D. (5,−3)

E. (5,−5)

NEW question from GMAT® Official Guide 2019

(PS02599)

Attachment: xy.jpg [ 13.82 KiB | Viewed 12433 times ]

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In the figure above, what are the coordinates of point R ?  [#permalink]

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9 I used the angle and length measurement to solve this. See my diagram below - I found this easiest.
##### General Discussion
Manager  S
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Re: In the figure above, what are the coordinates of point R ?  [#permalink]

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Bunuel wrote: In the figure above, what are the coordinates of point R ?

A. (3,−5)

B. (3,−3)

C. (5,5)

D. (5,−3)

E. (5,−5)

NEW question from GMAT® Official Guide 2019

(PS02599)

Attachment:
xy.jpg

We know that -

The line through point Q (5,3) is a vertical line with undefined slope. Thus, the x co-ordinate of the point R is 5.

Given that line through origin and point R is inclined 45 degree with the x-axis and it goes from left to right (bottom to top) - thus the slope is -1. Therefore, only if y co-ordinate is -5 will the slope of line OR be -1.

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Re: In the figure above, what are the coordinates of point R ?  [#permalink]

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3
1
The x-coordinate of R is positive and the y-coordinate of R is negative. So answer C is out.
The x-coordinate of R is the same with the x-coordinate of Q which is 5. So answer A and B are out.
The triangle of the 4th quartile has angles in the ratio 45:45:90 since there is a right angle at the point where the QR intersects the x-axis. So the ratio of the sides of the triangle is x:x:sqrt2*x. The x equals 5 since equals with the side PQ. But R is in the 4th quartile so we need the negative value which is -5. The coordinates of R are (5,-5)
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Re: In the figure above, what are the coordinates of point R ?  [#permalink]

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Dimensions of the rectangle would be height = 3 , width = 5

We know that it's a right angle triangle 90 - 45 (given) = 45 (the unknown angle)

So since we know that lets now operate on the following sine rule :

Sine A (angle) / a (opp side length) = Sine B (angle) / b (opp side length)

Applying the above rule :

Sine 45 / 5 = Sine 45 / x
(where x is the height of right angle triangle)

After computing we get x = 5.

Now the easiest part we know that right angle triangle is on negative side of Y Axis so it's -5 and we already know X Axis which is 5.

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Re: In the figure above, what are the coordinates of point R ?  [#permalink]

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Since the triangle has two 45 degree angles, is that enough to let you know that the base and height will be the same (i.e., R's x-value will be the same as Q)?
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Re: In the figure above, what are the coordinates of point R ?  [#permalink]

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royharmon4 wrote:
Since the triangle has two 45 degree angles, is that enough to let you know that the base and height will be the same (i.e., R's x-value will be the same as Q)?

Yes, it's enough to let us know the height since only base length is known we compute it with that.

The Law of Sines says that in any given triangle, the ratio of any side length to the sine of its opposite angle is the same for all three sides of the triangle. This is true for any triangle.

You can use the Law of Sines if you already know

> One side and its opposite angle, and
> One or more other sides or angles

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Re: In the figure above, what are the coordinates of point R ?  [#permalink]

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1
1
Bunuel wrote: In the figure above, what are the coordinates of point R ?

A. (3,−5)

B. (3,−3)

C. (5,5)

D. (5,−3)

E. (5,−5)

NEW question from GMAT® Official Guide 2019

(PS02599)

Attachment:
xy.jpg

OA: E
Equation of QR , $$x=5$$
Equation of OR , $$y=-x$$
The intersection point of Line QR and OR is R
Solving equation
$$x =5$$ and $$y=-x$$ , we get $$x=5$$ and $$y =-5$$
Coordinate of R $$: (5,-5)$$
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Re: In the figure above, what are the coordinates of point R ?  [#permalink]

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1
We know that sides in a 90-45-45 angle are in the ratio root 2:1:1. Notice the triangle is 90-45-45

From point Q(5,3) we know that the length of base of the triangle is 5. Hence the height will also be 5, while the hypotenuse will be 5root2.

Therefore, the x coordinate will be 5(base) and y coordinate will be -5( Height)

Ans- E
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Re: In the figure above, what are the coordinates of point R ?  [#permalink]

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Bunuel wrote: In the figure above, what are the coordinates of point R ?

A. (3,−5)

B. (3,−3)

C. (5,5)

D. (5,−3)

E. (5,−5)

NEW question from GMAT® Official Guide 2019

(PS02599)

IMO, no calculation was required, since in a PS question, the figures are drawn to scale.

Its even discussed here,https://gmatclub.com/forum/figures-drawn-to-scale-general-quant-question-279658.html

Only valid options were D and E.

Out of which only E wins, since the figure above the x axis will be a rectangle of area 15, which when inverted will make the same area.
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Re: In the figure above, what are the coordinates of point R ?  [#permalink]

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Bunuel wrote: In the figure above, what are the coordinates of point R ?

A. (3,−5)

B. (3,−3)

C. (5,5)

D. (5,−3)

E. (5,−5)

Attachment:
xy.jpg

Since the length of PQ is 5, the base of the triangle is 5. Since we have a 45-45-90 right triangle, the height is also 5. Since R has the same x-coordinate as Q, the coordinates of R are (5,-5).

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In the figure above, what are the coordinates of point R ?  [#permalink]

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Top Contributor
Bunuel wrote: In the figure above, what are the coordinates of point R ?

A. (3,−5)
B. (3,−3)
C. (5,5)
D. (5,−3)
E. (5,−5)
Attachment:
xy.jpg

One of my students asked for a more detailed solution. So, . . .

The coordinates of point Q give us information about the following lengths: Now focus on the RIGHT triangle below: We can see the missing angle is 45°, which makes this an ISOSCELES right triangle.

Since we have an ISOSCELES right triangle, we know the length of the other leg is 5 At this point, we have enough information to determine that point R has coordinates (5, -5) Cheers,
Brent
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Originally posted by GMATPrepNow on 05 May 2019, 08:57.
Last edited by GMATPrepNow on 13 May 2019, 08:57, edited 2 times in total.
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In the figure above, what are the coordinates of point R ?  [#permalink]

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Since 45:45:90. I mean two sides are equal, where one side is given 5

so, another equal side must be 5.

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Intern  B
Joined: 09 May 2019
Posts: 23
Re: In the figure above, what are the coordinates of point R ?  [#permalink]

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In the figure above, what are the coordinates of point R ?

A. (3,−5)

B. (3,−3)

C. (5,5)

D. (5,−3)

E. (5,−5)

Since we know both the angles opposite to the 90 degree angle are 45. So both the sides adjacent to the 90 degree angle should be equal.
Side on X axis we already know is 5.
So side parallel to Y axis is also 5
Hence coordinate - (5,-5) Re: In the figure above, what are the coordinates of point R ?   [#permalink] 18 Jul 2019, 03:59
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