In the figure above, what are the coordinates of point R ? : Problem Solving (PS)

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

25 Nov 2020, 12:40

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

21 Jun 2018, 10:01

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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)

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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.

Thus, answer E.

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

21 Jun 2018, 10:06

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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)
The correct answer is E.

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

13 Aug 2018, 07:54

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.

Therefore answer is 5,-5.

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

16 Aug 2018, 14:00

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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]

16 Aug 2018, 19:21

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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

Posted from my mobile device

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

17 Aug 2018, 01:30

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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)

Show Spoiler

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]

21 Aug 2018, 00:09

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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]

12 Feb 2019, 04:52

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

Updated on: 13 May 2019, 08:57

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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)

Show Spoiler

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)

Answer: E

Cheers,
Brent

Originally posted by BrentGMATPrepNow on 05 May 2019, 08:57.
Last edited by BrentGMATPrepNow 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]

06 May 2019, 01:09

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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.

And, Answer must be E

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

18 Jul 2019, 03:59

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)

Answer is 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)

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

27 Jan 2020, 12:17

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Given are two angles(45 and 90), R would be 45 deg, An isosceles right angled triangle.

- We get two sides of equal length, hence other side on y axis be also 5.
- Since it lies in 4th quadrant, coordinates will be (x, -y) form
- We get (5,-5)

Option E

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

24 Apr 2021, 10:19

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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)

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Answer: Option E

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

05 Jun 2021, 10:48

OR makes a 45 degrees angle with the origin, with a downward slope. So this is a y=-x line with slope -1.
Hence for every value of y, x= -y i.e. x and y have same numeric value but opposite signs.

There is only one answer choice fitting the two criteria - (5, -5)
Answer Choice: E

(Not sure if the question needed any calculation at all)

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

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

09 Aug 2023, 04:13

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

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