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Coordinate Geometry

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by swerve » Wed Jan 22, 2020 12:00 pm
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

The OA is E

Source: Magoosh
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Re: Coordinate Geometry

by Jay@ManhattanReview » Thu Jan 23, 2020 12:14 am
swerve wrote: ↑
Wed Jan 22, 2020 12:00 pm
 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

The OA is E

Source: Magoosh
Given that B = (–1, –1) and C = (5, 2), the mid-point of BC is [(–1 + 5)/2, (–1 + 2)/2)] = (2, 1/2)

The endpoints of the referred median are (2, 1/2) and (0, 5). The slop of a line whose coordinates are (x, y) and (a, b) is given by (y – b)/(x – a).

Thus, the slope of the referred median = (5 – 1/2)/(0 – 2) = (9/2)/(–2) = –9/4

The correct answer: E

Hope this helps!

-Jay
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