M(-4,-2) is the midpoint of RS. If S has coordinates (-2,5), find the coordinates of R.

Midpoint formula:

M = [ (x1 + x2)/2 , (y1 + y2)/2]

(-4,2) = [ (-2 + x)/2 , (5, + y)/2 ]

-4 = (-2 + x)/2 and 2 = (5 + y)/2
-8 = -2 + x. and 4 = 5 + y
-6 = x. and -1 = y

Coordinates of R (-6, -1)

To find the coordinates of point R, we need to use the midpoint formula. The midpoint formula states that the coordinates of the midpoint between two points (x₁, y₁) and (x₂, y₂) is given by the following formulas:

Midpoint x-coordinate = (x₁ + x₂) / 2
Midpoint y-coordinate = (y₁ + y₂) / 2

Given that M(-4, -2) is the midpoint of RS, and S has coordinates (-2, 5), we can set up the following equation:

Midpoint x-coordinate = (x₁ + (-2)) / 2 (1)
Midpoint y-coordinate = (y₁ + 5) / 2 (2)

Substituting the coordinates of M into the above equations, we get:

-4 = (x₁ + (-2)) / 2 (1)
-2 = (y₁ + 5) / 2 (2)

Using cross-multiplication, we can solve for x₁ and y₁:

1. From equation (1):
-4 * 2 = x₁ + (-2)
-8 + 2 = x₁
x₁ = -6

2. From equation (2):
-2 * 2 = y₁ + 5
-4 - 5 = y₁
y₁ = -9

Therefore, the coordinates of point R are (-6, -9).

To find the coordinates of R, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint (M) between two points (R and S) can be found by taking the average of their x-coordinates and the average of their y-coordinates.

Let's denote the coordinates of R as (x, y). We know that M is the midpoint of RS, so we can set up the following equations:

Midpoint formulas:
(x + (-2))/2 = -4
(y + 5)/2 = -2

Simplifying the equations, we have:
(x - 2)/2 = -4
(y + 5)/2 = -2

Now, we can solve these equations to find the values of x and y.

For the first equation, multiply both sides by 2:
x - 2 = -8

Add 2 to both sides:
x = -8 + 2
x = -6

For the second equation, multiply both sides by 2:
y + 5 = -4

Subtract 5 from both sides:
y = -4 - 5
y = -9

Therefore, the coordinates of R are (-6, -9).