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The median of a triangle is the line from any vertex to the midpoint o

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The median of a triangle is the line from any vertex to the midpoint o  [#permalink]

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New post 04 Mar 2015, 04:18
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The median of a triangle is the line from any vertex to the midpoint of the opposite side. Triangle ABC has vertices A = (0, 5), B = (–1, –1), and C = (5, 2). What is the slope of the median from A to the midpoint of BC?

A. –3/4
B. –4/3
C. –5
D. –5/2
E. –9/4



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Re: The median of a triangle is the line from any vertex to the midpoint o  [#permalink]

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New post 08 Mar 2015, 14:44
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Bunuel wrote:
The median of a triangle is the line from any vertex to the midpoint of the opposite side. Triangle ABC has vertices A = (0, 5), B = (–1, –1), and C = (5, 2). What is the slope of the median from A to the midpoint of BC?

A. –3/4
B. –4/3
C. –5
D. –5/2
E. –9/4



Kudos for a correct solution.


For your visual understanding, here’s a diagram of the situation.
Image

First to find the midpoint of B & C — average the x-coordinates: (–1+ 5)/2 = 2; and average the y-coordinates: (–1 + 2)/2 = 1/2. Thus, the midpoint has coordinates (2, 1/2). We want the slope from A = (0, 5) to (2, 1/2). The rise is the change in the y-coordinates: 1/2 – 5 = -9/2. The run is the change in the x-coordinates: 2 – 0 = 2. Slope = rise/run = [–9/2]/2 = –9/4.

Answer = (E)
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Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: The median of a triangle is the line from any vertex to the midpoint o  [#permalink]

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New post 27 Jun 2016, 10:53
I don't understand why can't we use the slope of AB, so 1/2 and it's negative inverse to get the perpendicular slope, so -2 ?..
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Re: The median of a triangle is the line from any vertex to the midpoint o  [#permalink]

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New post 19 Jan 2018, 05:32
iliavko wrote:
I don't understand why can't we use the slope of AB, so 1/2 and it's negative inverse to get the perpendicular slope, so -2 ?..


I have supposed that you mean slope BC that it is 1/2. The reason why the slope of the median it is not -2, it is because BC and the median are not perpendicular, they only have to cut in the mid-point, which doesn't mean that they are perpendicular. If the would be perpendicular you would be right
Re: The median of a triangle is the line from any vertex to the midpoint o &nbs [#permalink] 19 Jan 2018, 05:32
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