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In the figure above, segments PQ and QR are each parallel to one of th

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Bunuel
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In the figure above, segments PQ and QR are each parallel to one of th [#permalink] New post   20 Jul 2020, 01:09
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In the figure above, segments PQ and QR are each parallel to one of the coordinate axes. What is the ratio of the length of QR to PQ?

(1) The slope of the line that passes through points P and R is 0.75.

(2) The coordinates of point P are (4, 2)



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Re: In the figure above, segments PQ and QR are each parallel to one of th [#permalink] New post   20 Jul 2020, 01:32
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Statement 1: Slope is nothing but the ratio of y2-y1/x2-x1 also known as rise/run ratio or the two legs of the right angle triangle given in the question.
Slope = Y2-y1 (PQ) / x2-x1 (QR)
0.75 = PQ/QR
3/4 = PQ/QR
PQ:QR = 3:4
(Sufficient)

Statement 2: slope is not given we can have infinite values of slope from point P. (Insufficient)

IMO A

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Re: In the figure above, segments PQ and QR are each parallel to one of th [#permalink] New post   20 Jul 2020, 02:47
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IMO A.

Slope is basically rise of y with respect to x.
(y2-y1)/(x2-x1)= slope.
So knowing the slope, we know the ratio QP/QR.
A is sufficient.

B gives the coordinate of P. Since the line doesn't pass thru origin, we can't be sure of the slope from just one point.
B is not sufficient.

Answer A
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Re: In the figure above, segments PQ and QR are each parallel to one of th [#permalink] New post   20 Jul 2020, 20:42
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1) slope =0.75 = 3/4
PQ/QR=3/4
QR/PQ=4/3
sufficient

2) using one point P alone, not possible
insufficient

Ans A
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Re: In the figure above, segments PQ and QR are each parallel to one of th [#permalink] New post   20 Jul 2020, 03:21
We need to find the ratio of the length of QR to PQ.

Statements:

(1) The slope of the line that passes through points P and R is 0.75

Slope = y/x. Since both segments, PQ and QR are each parallel to one of the coordinate axes. Triangle PQR becomes a right angle triangle and angle PRQ is equal to angle formed by line segment PR and x axis.
Hence, as we already know the slope, we can find the ratio of lengths of PQ and QR.

Sufficient.

(2) P = 4,2

There can be multiple lines that can pass through P of different slopes.

Insufficient

Hence, the answer is Option (A).
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Re: In the figure above, segments PQ and QR are each parallel to one of th [#permalink] New post   20 Jul 2020, 10:54
By its very definition, slope refers to the vertical distance between any two points on the line divided by the horizontal distance between those two points

What the question asks is the ratio of QR to PQ, which is precisely negative of the reciprocal of the slope of the given line. Hence only the value of slope is sufficient to answer the question

Answer: A
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Re: In the figure above, segments PQ and QR are each parallel to one of th [#permalink] New post   31 May 2023, 08:39
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Re: In the figure above, segments PQ and QR are each parallel to one of th [#permalink]
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