Line L and line K have slopes -2 and 1/2 respectively. If line L and l

Question

Line L and line K have slopes -2 and 1/2 respectively. If line L and line K intersect at (6,8), what is the distance between the x-intercept of line L and the y-intercept of line K?

A) 5
B) 10
C)  5\sqrt{5} 
D) 15
E)  10\sqrt{5}

Source: GMAT Prep Now

ENGRTOMBA2018 · Answer

Follow the posting guidelines.

As for your question, "Is there a nice fast solution?", it is not going to be helpful either to you or any other member when you ask such questions without providing information as to what did you do to approach this question. It is fine to ask an "alternate method" but to talk about "fastest" or "easiest" is going to defeat the purpose of having a useful discussion.

The classic way is:

Assume the equations of the 2 lines, L and K as

y=-2x+a and
y=x/2 +b respectively

As both these lines pass through (6,8), substitute x=6 and y=8 to get the values of a and b as 20 and 5 respectively.

Thus equations of the 2 lines become

L: y=-2x+20, x-intercept = (10,0) and
K: y=x/2 +5, y-intercept = (0,5) respectively

Thus the distance = distance between (10,0) and (0,5) =  \sqrt {(10-0)^2+(0-5)^2}  =  5\sqrt{5} . C is the correct answer.

skylimit · Answer

I agree. However, the site doesn't allow links in posts for first 5 days and this makes it hard. I didn't know how to solve the question. When I checked the video solution I thought it was too long of an approach. So, I asked for a shorter solution. I guess I could have entered the complete solution from the video, but that seemed like a waste.

Thanks for your solution though. It's basically the same as the one in the video

ENGRTOMBA2018 · Answer

The solution above is per the basics of coordinate geometry and lines and took me all of 1.2 minute to solve this question. How much more quickly do you want to solve such a question? This question seems to be 650-700 level (more so towards 700) and thus would need you to apply a number of connected concepts in a particular form. I do believe that a graphical method would have been more straightforward (not quicker!) had the question asked for the area of the triangle formed by the 2 lines and the X-axis.

mvictor · Answer

my approach: plug in values for each equation
y=-2x+b => 8=-2*6 +b -> b=20
y=x/2+b => 8=6/2 +b => b=5 (Y INTERCEPT OF THE LINE K)

now, let's find for x intercept of line L.
y must be zero
0=-2x+20 -> x=10

so we have a right triangle with leg 5 and 10. the distance between these two points is: sqrt(5^2 + 10^2) = sqrt(125) = 5*sqrt(5)

C

KarishmaB · Answer

You can also use the concept of slope.

Slope = -2 means that for every 1 unit increase in x co-ordinate, y co-ordinate decreases by 2. Line L has slope -2 and passes through (6, 8). It's x intercept will have y = 0 i.e. a decrease of 8 so x will increase by 4 to 6 + 4 = 10. So x intercept is 10.

Line K has slope 1/2 and passes through (6, 8). It's y intercept will have x = 0 i.e. a decrease of 6 so y will decrease by 1/2 of that i.e. by 3. So y intercept is 8 - 3 = 5.

Distance between the two points can be found using pythagorean theorem as  \sqrt{10^2 + 5^2} = 5\sqrt{5} .

Answer (C)

sahilvijay · Answer

Answer is clearly C  as shown in figure.

finisher009 · Answer

The Fast (2-Step Solution)

1. Find the Intercepts:
 • X-intercept of Line L (slope -2): An x-intercept means y=0. Starting from the intersection point (6,8), to get y down to 0, you need to go down by 8. Since the slope is -2 (rise/run), a “rise” of -8 means a “run” of +4. So, the x-coordinate is 6 + 4 = 10. The point is (10, 0).
 • Y-intercept of Line K (slope 1/2): A y-intercept means x=0. Starting from (6,8), to get x down to 0, you need to go left by 6. Since the slope is 1/2 (rise/run), a “run” of -6 means a “rise” of -3. So, the y-coordinate is 8 - 3 = 5. The point is (0, 5).

2. Calculate the Distance:
 • Use the distance formula between (10, 0) and (0, 5).
 • Distance = sqrt( (10-0)^2 + (0-5)^2 )
 • Distance = sqrt( 100 + 25 ) = sqrt(125)
 • Simplify: sqrt(125) = sqrt(25 * 5) = 5 * sqrt(5).

This matches answer choice C.

Line L and line K have slopes -2 and 1/2 respectively. If line L and l

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GMAT Problem Solving (PS) Questions

Line L and line K have slopes -2 and 1/2 respectively. If line L and l

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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