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Math Expert V
Joined: 02 Sep 2009
Posts: 58381
The median of a triangle is the line from any vertex to the midpoint o  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 71% (02:18) correct 29% (02:51) wrong based on 199 sessions

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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

Kudos for a correct solution.

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Math Expert V
Joined: 02 Sep 2009
Posts: 58381
Re: The median of a triangle is the line from any vertex to the midpoint o  [#permalink]

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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. 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.

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General Discussion
Senior Manager  S
Joined: 08 Dec 2015
Posts: 285
GMAT 1: 600 Q44 V27 Re: The median of a triangle is the line from any vertex to the midpoint o  [#permalink]

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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 ?..
Intern  B
Joined: 25 Sep 2017
Posts: 2
Location: Spain
GPA: 3.15
WE: Consulting (Consulting)
Re: The median of a triangle is the line from any vertex to the midpoint o  [#permalink]

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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   [#permalink] 19 Jan 2018, 05:32
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