Question

ОЧЕНЬ СРОЧНО!!!! Знайдіть довжину медіани АМ трикутника АВС, якщо А(-3; 1), В(2; -2), C(-4;6)​

Answer 1

Ответ:

Удачи

Объяснение:

Δ АВС

Медіана йде до сторони BC,з кута А

Тоді

х(середини)=(х₁+х₂):2 і

(y₁+y₂):2

Нехай данна медіана-AM

звідси за формулой:=(2+(-4):2= -1

y=(-2-4):2= -3

М=(-1;-3)

|АМ|= $\sqrt{((-1+3)^{2}+(-3+1)^{2} }$

|АМ|= $\sqrt{8}$

АМ=$2\sqrt{2}$

Answer 2

Finding the Length of the Median AM of Triangle ABC

To find the length of the median to the side BC of triangle ABC, we first need to identify the vertices of the triangle. The vertices given are:

- A(-3, 1) - B(2, -2) - C(-4, 6)

The median to a side of a triangle is the line segment joining a vertex to the midpoint of the opposite side. To find the midpoint of BC, we take the average of the x-coordinates and y-coordinates of B and C:

Midpoint of BC = ((2 + (-4))/2, (-2 + 6)/2) = (-1, 2)

Now we can use the distance formula to calculate the length of the median:

d = √(x2 - x1)2 + (y2 - y1)2

Where: x1, y1 are the coordinates of the vertex (in this case A) x2, y2 are the coordinates of the midpoint

Plugging in the values:

d = √((-3 - (-1))2 + (1 - 2)2) = √(2)2 + (-1)2 = √4 + 1 = √5

Therefore, the length of the median to the side BC of triangle ABC is √5 units.