GMAT Club Around The World!!! In the coordinate plane above, if line

Question

https://gmatclub.com/forum/download/file.php?id=59269 In the coordinate plane above, if line 1 || line 2 || x-axis and point a on line 2 is exactly 13 units away from point b on line 1, what is the x-coordinate of point b ? A. 19 B. 17 C. 15 D. 12 E. 8 Happy New Year Australia, Federated States of Micronesia, France/New Caledonia, Papua New Guinea/Autonomous Region of Bougainville, Solomon Islands, and Vanuatu! Dec 31 Event: GMAT Club Around The World ! (38 new questions posted every hour time zone on Dec 31!) https://gmatclub.com/forum/download/file.php?id=59744 1.jpg

yashikaaggarwal · Answer

Distance between two points A(X1,3) and B(X2,8) = 13
D = √(X2-X1)^2+(Y2-Y1)^2
13 = √(X2-X1)^2+(8-3)^2
169 = (X2-X1)^2+5^2
169-25 = (X2-X1)^2
144 = (X2-X1)^2
12 = (X2-X1)

Now, X1 of A = 7
X2 = 12+7
X2 = 19

Answer is A

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rocky620 · Answer

Kindly refer the image below:

Lets drop a perpendicular  c  from point  b  to l2

AB = 13
BC= (8-3) = 5
So, AC will be 12.

x co-ordinate of b  = distance of  a  from y-axis+AC => 7+12 = 19

IMO Option A

Deepakjhamb · Answer

In the coordinate plane above, if line 1 || line 2 || x-axis and point a on line 2 is exactly 13 units away from point b on line 1, what is the x-coordinate of point b ?

A. 19
B. 17
C. 15
D. 12
E. 8

x coordinate b = 7 + underroot (13^2- 5^2) = 7+ 12 = 19

ans = A)19

bidskamikaze · Answer

Point a is 13 units away from point b, so we get a right triangle with hypotenuse = 13.
The perpendicular distance between line a and line b is 8-3 = 5.
So, the horizontal distance must be 12 units (Pythagorean triplets).
Point b must be 12 + 7 = 19 units away from origin. Therefore, its x- coordinate should also be 19.

Answer A.

BIDJI23 · Answer

Can't wait to read the explanations here. I have no precise method...

I guess it's  C .

Harsh9676 · Answer

Ans A

Equation of Line 1 Y = 8 and Line 2 is Y = 3

The Y co-ordinate of each of the lines is 8 for L1 and 3 for L2

So Point a = (7,3) and b = (X, 8)

Given the distance between a and b is 13

Therefore Sqrt((X-7)^2 * (8-3)^2) = 13

>> X^2 - 14X - 95 = 0

>> X = 19 or -5

In PS questions, we can trust the figure given unless otherwise is specified. Point b is in Q1, so X cannot be negative.

anjanita · Answer

The answer is A

The vertical distance between a & b is 5 unit and the hypotenuse is 13, therefore the horizontal distance is √(169-25) = 12

So, x-coordinate of point b is 7+12 = 19

ananya3 · Answer

IMO A

distance between a and b = 13
triangle ABC is a right angle triangle right angled at B
AC = 13
BC = 8 - 3 = 5
AB =  √13^2-5^2  = 12
x coordinate of b = x coordinate of B = x coordinate of a + AB = 7 + 12 =  19

TarunKumar1234 · Answer

Given, distance between a and b= 13 a= (7,3), so, 13^2 = (x-7)^2 + (8-3)^2 or, (x-7)^2 = 169-25= 144, x-7= 12, (consider in positive x) so, x= 19. So, I think A.

Aks111 · Answer

The straight line between a and b forms the hypotenuse of a right angled triangle formed by perpendicular line from b to line l1, whose length is given as 13 units.
The vertical distance between l1 and l2 is difference in y co-ordinates i.e. 8-3 = 5.
The horizontal distance between a and b will be  \sqrt{13^2 - 5^2} = \sqrt{12^2} 
Thus the x co-ordinate of b will be x co-ordinate of a (7) + 12 = 19.
 Answer: A

mdsaddamforgmat · Answer

IMO:A = 19
Given, distance btw A & B is 13units i.e. the shortest distance.
Hence, according to Pythagoras theorem => 13^2 = 5^2+(horizontal distance btw A & B)^2
 horizontal distance btw A & B = 12
 therefore, x unit of B = 12+7 = 19

Green2k1 · Answer

Correct Answer A

Coordinate of a( 7, 3) and b (x+7, 8)
it will form the right angle triangle 
D = 13
13^2 = 5^2 +x^2
x = 12

X coordinate of b = 12+7 = 19

Neha2404 · Answer

ImoA

If a point is 13 unit away 
Means
13^2=5^2-x^2
X=12

B cordinate of x=12+7=19

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manasi05 · Answer

From the figure, we know that y coordinate of line 1 is 8 and it will be 8 for all points on the line as its a horizontal line parallel to the x-axis
Same way y coordinate of line 2 is 3 and it will be 3 for all points on the line as its a horizontal line parallel to the x-axis
From the figure, we also know that the x coordinate for a is 7

The distance between a and b is 13

So using the distance between 2 points formula we can write
13 = √(x-7)^2 +(8-3)^2
13^2 = (x-7)^2 + 5^2
169 = x^2 +49 -14x +25
169 = x^2 -14x + 74
x^2 -14x -95 = 0
(x-19) (x+5) = 0
x = 19 , -5

Since point b is in the first quadrant so the value of x will be positive which is 19

Hence the answer will be A

MakSha · Answer

Let the x-coordinate of point b be x.

Co-ordinates of point A: (7,3) and point B: (x,8).

From the diagram and information provided in the question statement:

(x-7)^2 + (8-3)^2 = (13)^2

-> (x-7)^2 = (12)^2
-> x-7 = 12 / -12
-> x = 19 /-5

Since, point B is in the first quadrant, x>0.
thus, x = 19.

IMO, option A is the answer.

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GMAT Club Around The World!!! In the coordinate plane above, if line

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