Question

A(-2;4) B(10;-1) C(6;-4) Найти AB-? BC-? BK-медиану K(x;y)

Answer 1

Ответ:

на фото

Объяснение:

Answer 2

To find the lengths of AB, BC, and the median BK, we can use the distance formula between two points in a coordinate plane.

The distance formula is given by: d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Let's calculate the lengths of AB and BC:

Length of AB: A(-2, 4) B(10, -1)

AB = sqrt((10 - (-2))^2 + (-1 - 4)^2) = sqrt((12)^2 + (-5)^2) = sqrt(144 + 25) = sqrt(169) = 13

So, the length of AB is 13 units.

Length of BC: B(10, -1) C(6, -4)

BC = sqrt((6 - 10)^2 + (-4 - (-1))^2) = sqrt((-4)^2 + (-3)^2) = sqrt(16 + 9) = sqrt(25) = 5

So, the length of BC is 5 units.

Now, let's find the coordinates of the midpoint K and then calculate the length of BK:

Midpoint K: K = ((Bx + Cx) / 2, (By + Cy) / 2) = ((10 + 6) / 2, (-1 + (-4)) / 2) = (16 / 2, -5 / 2) = (8, -2.5)

So, the coordinates of the midpoint K are (8, -2.5).

Length of BK: B(10, -1) K(8, -2.5)

BK = sqrt((8 - 10)^2 + (-2.5 - (-1))^2) = sqrt((-2)^2 + (-1.5)^2) = sqrt(4 + 2.25) = sqrt(6.25) = 2.5

So, the length of BK is 2.5 units.