Question

Какие кардинаты имеет точка,симметрична точке А(2;-4)относительно точке М(3;-1)?

Answer 1

Координаты вектора MA = { (2-3);(-4)-1 } = (-1;-3)
Симметричная точка должна получаться перемещением точки M на вектор -MA
A'= (3;-1)+(1;3)=(4;2)

Answer 2

Coordinates of the Point Symmetric to Point A(2,-4) with Respect to Point M(3,-1)

To find the coordinates of the point symmetric to point A(2,-4) with respect to point M(3,-1), we can use the midpoint formula and the distance formula.

The midpoint formula is given by: Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

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

Let's calculate the coordinates of the point symmetric to point A(2,-4) with respect to point M(3,-1).

First, we need to find the midpoint of points A and M: Midpoint = ((2 + 3) / 2, (-4 + (-1)) / 2) Midpoint = (2.5, -2.5)

Next, we calculate the distance between points A and M: Distance = √((3 - 2)^2 + (-1 - (-4))^2) Distance = √(1 + 9) Distance = √10

Now, we can find the coordinates of the point symmetric to point A with respect to point M using the midpoint and distance: New point = Midpoint + Midpoint - A New point = (2.5, -2.5) + (2.5 - 2, -2.5 - (-4)) New point = (2.5, -2.5) + (0.5, 1.5) New point = (3, -1)

Therefore, the coordinates of the point symmetric to point A(2,-4) with respect to point M(3,-1) are (3, -1).