GMAT Official Guide 2019 In the figure above, what

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Wed Jun 27, 2018 7:26 pm

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

A. (3,âˆ’5)

B. (3,âˆ’3)

C. (5,5)

D. (5,âˆ’3)

E. (5,âˆ’5)

Last edited by BTGmoderatorDC on Sat Jun 30, 2018 11:13 pm, edited 1 time in total.

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Source: Beat The GMAT — Problem Solving | Wed Jun 27, 2018 7:26 pm

Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Thu Jun 28, 2018 2:27 am

Hello BTGmoderatorDC.

Let's take a look at your question.

Let's call R(x,y).

Here, since the point R is in a vertical line that passes through the point Q(5,3), the x-coordinate of R is equal to 5 (x=5).

Now, we just have to find the value of y.

We can do it in two different ways:

1. We can see a right triangle with one angle equal to 45Âº, so the other angle will be also 45Âº. So, this triangle is isosceles.

Therefore, the other cathetus is equal to 5, that is to say, y=-5.

So, the coordinates of R are (5,-5).

2. Since the line that passes through r and the origin makes an angle of 45Âº with the x-axis, then this line is y=-x.

Therefore, the coordinates of R are (x,-x). Since we know x=5 then R(5,-5).

In any case, we get that the correct answer is the option E.

I hope it helps you. <i class="em em-smiley"></i>

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8152; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Mon Apr 29, 2019 8:09 am

BTGmoderatorDC wrote:

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

A. (3,âˆ’5)

B. (3,âˆ’3)

C. (5,5)

D. (5,âˆ’3)

E. (5,âˆ’5)

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).

Answer: E

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