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The coordinates of the vertices of a scalene triangle are A (0, 0), B (2, 2), and          C (6, –6). What is the equation of the median from vertex A?  1 pointA. x – 2y = 0B. 2x – y = 0C. x + 2y = 0D. 2x + y = 0BackNext

Question

The coordinates of the vertices of a scalene triangle are A (0, 0), B (2, 2), and          C (6, –6). What is the equation of the median from vertex A?  1 pointA. x – 2y = 0B. 2x – y = 0C. x + 2y = 0D. 2x + y = 0BackNext

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Solution

The median of a triangle from a given vertex is a line segment joining the vertex to the midpoint of the opposite side.

First, let's find the midpoint of the line segment BC. The midpoint formula is ((x1+x2)/2, (y1+y2)/2).

So, the midpoint, M, of BC is ((2+6)/2, (2-6)/2) = (4, -2).

Now, we need to find the equation of the line AM. The slope of a line is given by (y2-y1)/(x2-x1).

So, the slope of AM is (-2-0)/(4-0) = -1/2.

The equation of a line is y = mx + c, where m is the slope and c is the y-intercept. Since the line passes through the origin (0,0), the y-intercept is 0.

So, the equation of the line is y = -1/2x + 0, or 2y = -x.

Rearranging, we get x + 2y = 0.

So, the correct answer is C. x + 2y = 0.

This problem has been solved

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