Q44. Math PS - Coordinate geometry slopes

Q. The product of slopes of two lines L1 and L2 is -1. If the lines intersect at point (2,-2) and the x intercept of line L1 is 8, what is the y intercept of line L2?

A) 12
B) -12
C) 8/3
D) -8/3
E) None of the above


Difficulty Level : Medium
Time to Solve : <70 secs


Please discuss your approach and also provide time you took to solve the question.

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2/6=1/3
x=-3, no such answer. so it's E

For me the y intercept comes out to be 4

Hence E.

e

E - 60 secs.

Solution:


Given Information:
M1*M2 = -1
(2,-2) is a point both lines share
X1 = 8
Given Equations:
(L1) Y1=M1*X1 + B1
(L2) Y2 = M2*X2 + B2
(1) M2 = -1/M1
Plug in (8, 0) from given information into (L1)
(2) M1 = -B1/8
Plug equation (2) into (1):
(3) M2 = 8/B1
Plug (2,-2) and equation (2) into (L1) to find B1:
(4) B1 = -8/3
Plug equation (4) into (3):
(5) M2 = 3
Plug (2,-2) and equation (5) into L2 to solve for B2
B2 = 4
Therefore Answer E is correct.

Couldn't understand. M2 is 3 in your solution. M1=-B1/8=-(-8/3)/8=1/3. but here M2*M1=3*1/3=1, not -1
Can you just say what's the value of the second slope. Of the first is 1/3 and of the second is -3?

Clerk,

I copied my work into the message box wrong. I have -3 wrote down on my paper but I typed 3 when I was posting my answer. M2 = 8*3/(-8) = -3. Thanks.

From a theoretical point of view, given the equation M1*M2 = -1

Equation (2) calculates M1 to be –B1/8
Equation (3) calculates M2 to be 8/B1.

Thus, (-B1/8)*(8/B1) = -1 for all non-zero values of B1.

Sure, I know that is a misprint. Thank you

e

OA E:

The traditional way to do this:

L1 passes through points (2,-2) and (8,0)

slope of L1 = 2/6 = 1/3

Since L1*L2 = -1 => L2 = -3

So slope intercept equation of L2 =
y = -3x + c

it passes through (-2,2) =>
-2 = -6 + c => C = 4 (Y intercept is 4)

The trick to the question is knowing to use the correct forms of equation of line to save time.


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Using backsolving:
L1 passes through points (2,-2) and (8,0) => slope of L1 = 1/2 .. so slope of L2 must be -3 ... We know L2 passes through (-2,2) lets take each choice which represents Y intercept hence point (0,y)

A) (0,12) .. slope = (12-2)/(0+2) = 5 NO
B) (0,-12) .. slope = -5 (no need to calculate, just see from above)
C) (0,8/3) = (8/3 - 2)/(0+2) = something with 3 in denominator. no
D) (0,-8/3) = ... there will still be 3 in denominator .. no

Has to be E

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I deally, seeing that 12 didnt work, I wouldnt even have considered -12 and similarly for 8/3 ... This is a good example where using backsolving in the GMAT Test may save you a few precious seconds in the . However it doesn't help that the answer is "none of these" it may lead to second guessing so be careful.

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