Question

AD- медіана трикутника з вершинами А(0;7), В(5;-2), C(11;4). Запишіть рівняння прямої AD.​

Answer 1

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To find the equation of line AD, we first need to find the coordinates of point D, which is the midpoint of side BC.

The coordinates of B are (5,-2) and the coordinates of C are (11,4).

The midpoint formula is:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

So, the coordinates of D are:

D = ((5+11)/2, (-2+4)/2) = (8,1)

Now that we have the coordinates of point D, we can find the slope of line AD using the slope formula:

Slope = (y2 - y1)/(x2 - x1)

Let A be the point (0,7), so:

Slope = (1 - 7)/(8 - 0) = -6/8 = -3/4

Finally, we can use the point-slope form of a line to write the equation of line AD:

y - 7 = (-3/4)(x - 0)

Simplifying:

y = (-3/4)x + 7

Therefore, the equation of line AD is y = (-3/4)x + 7.