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

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

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21 Jun 2018, 08:44
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79% (00:50) correct 21% (00:39) wrong based on 672 sessions

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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)

NEW question from GMAT® Official Guide 2019

(PS02599)

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xy.jpg [ 13.82 KiB | Viewed 4232 times ]

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

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21 Jun 2018, 09:01
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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21 Jun 2018, 09:06
3
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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13 Aug 2018, 06:54
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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16 Aug 2018, 13:00
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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16 Aug 2018, 18:21
1
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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17 Aug 2018, 00:30
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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20 Aug 2018, 23:09
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)

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

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19 Nov 2018, 15:09
1

I used the angle and length measurement to solve this. See my diagram below - I found this easiest.
In the figure above, what are the coordinates of point R ? &nbs [#permalink] 19 Nov 2018, 15:09
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# In the figure above, what are the coordinates of point R ?

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