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If OB=AB=5 and OA=6, what is the slope of the line passing through A a

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If OB=AB=5 and OA=6, what is the slope of the line passing through A a [#permalink]

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If OB=AB=5 and OA=6, what is the slope of the line passing through A and B?

A. 4/3
B. 5/6
C. 4/5
D. 2/3
E. −5/3
[Reveal] Spoiler: OA

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Re: If OB=AB=5 and OA=6, what is the slope of the line passing through A a [#permalink]

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See attached figure.

For an isosceles triangle perpendicular from the vertex B to the unequal side OA (base) will divide the triangle into two equal halves.
i.e C is the midpoint of OA and point C is (3,0)

BC = 4 ; This can be easily seen by applying Pythagoras theorem to the triangle OCB , (3,4,5 is a Pythagorean triplet.)
So point B will be (3,-4) and point A is (6,0)

Slope of line AB = (y2 - y1)/ (x2 - x1)
= (0 - -4)/ (6 -3)
= 4/3

Answer A

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Re: If OB=AB=5 and OA=6, what is the slope of the line passing through A a [#permalink]

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New post 21 Oct 2017, 02:00
There is an even quicker way to solve this problem. Looking at the answer choices there is only one that is bigger than 1. Therefore that's the right one.

Why? Because the y coordinate increases at a higher rate than the x coordinate for the segment BA. If the rate would have been the same, the slope will be equal to 1.

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If OB=AB=5 and OA=6, what is the slope of the line passing through A a [#permalink]

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New post 21 Oct 2017, 13:46
Ed_Palencia wrote:
There is an even quicker way to solve this problem. Looking at the answer choices there is only one that is bigger than 1. Therefore that's the right one.

Why? Because the y coordinate increases at a higher rate than the x coordinate for the segment BA. If the rate would have been the same, the slope will be equal to 1.

Ed_Palencia - how did you conclude that the slope is greater than 1?

Did you conclude that without bisecting the isosceles triangle, such that you get sides 3-4-5 and can see that rise, which is 4, is greater than run, which is 3, i.e. slope = \(\frac{4}{3}\)?

I can't see any other way to detect slope; if that is the case, then we know that the slope is \(\frac{4}{3}\), exactly, anyway. What am I missing?

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Re: If OB=AB=5 and OA=6, what is the slope of the line passing through A a [#permalink]

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genxer123 wrote:
Ed_Palencia wrote:
There is an even quicker way to solve this problem. Looking at the answer choices there is only one that is bigger than 1. Therefore that's the right one.

Why? Because the y coordinate increases at a higher rate than the x coordinate for the segment BA. If the rate would have been the same, the slope will be equal to 1.

Ed_Palencia - how did you conclude that the slope is greater than 1?

Did you conclude that without bisecting the isosceles triangle, such that you get sides 3-4-5 and can see that rise, which is 4, is greater than run, which is 3, i.e. slope = \(\frac{4}{3}\)?

I can't see any other way to detect slope; if that is the case, then we know that the slope is \(\frac{4}{3}\), exactly, anyway. What am I missing?


Yes, I forgot to mention the implied triangle triple 3:4:5 in order to derive the conclusion. My apologies about that

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Re: If OB=AB=5 and OA=6, what is the slope of the line passing through A a [#permalink]

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New post 26 Oct 2017, 18:45
Alternatively, we know that O(0,0) and A(6,0) and we also know that distance between AB and OB is 5.

So as this point B is in the 4th quadrant, the point will be of the form B(x,-y).

by applying the distance formulas we will get OB = X^2 + Y^2 = 25 ....(1)
and AB = X^2+Y^2+36-12x = 25 ...(2)

Equating both and solving,we will get B(3,-4).Since we now know A(6,0) and B(3,-4), we can find the slope.

Thanks,
Sid

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Re: If OB=AB=5 and OA=6, what is the slope of the line passing through A a   [#permalink] 26 Oct 2017, 18:45
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