the coordinates of point S are given. the midpoing of RS is (6,-10). find the coordinates of point r. s(0,8)
If we let M be the midpoint,
S-M = (0,8) - (6,-10) = (-6,18)
that means that M-R must also be (-6,18), or R = M-(-6,18)
R = (6,-10) - (-6,18) = (12,-28)
To find the coordinates of point R, we need to understand that the midpoint of RS, which is (6, -10), is the average of the x-coordinates and the average of the y-coordinates of R and S.
Given that the coordinates of S are (0, 8), let's denote the coordinates of R as (x, y).
The midpoint formula can be written as:
Midpoint = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
Now, let's substitute the known values into the formula:
(6, -10) = ((x + 0) / 2, (y + 8) / 2)
Simplifying:
6 = (x / 2)
-10 = (y + 8) / 2
To isolate x, we can multiply both sides of the first equation by 2:
12 = x
To isolate y, we can multiply both sides of the second equation by 2:
-20 = y + 8
-20 - 8 = y
-28 = y
Therefore, the coordinates of point R are (12, -28).