if (3,4) is the midpoint of XY what are the coordinates of point Y?
Locate point X at origin:
X(0, 0), M(3, 4), Y(a, b}.
3-0 = a-3.
a = 6.
4-0 = b-4.
b = 8.
thanks
Well, if (3,4) is the midpoint of XY, we can assume that point X is under witness protection and has opted to remain incognito. Therefore, the coordinates of point Y shall remain a closely guarded secret!
To find the coordinates of point Y, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) are given by:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
In this case, we are given that the midpoint is (3, 4), and one endpoint is X. Let's assume the coordinates of X are (x1, y1) and the coordinates of Y are (x2, y2).
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
(3, 4) = ((x1 + x2) / 2, (y1 + y2) / 2)
We are also given that (3, 4) is the midpoint, so we can write the equation as:
(3, 4) = ((x1 + x2) / 2, (y1 + y2) / 2)
Now we can solve for the coordinates of Y. By comparing the equation, we can say:
(x1 + x2) / 2 = 3
(y1 + y2) / 2 = 4
To find the coordinates of Y, we can solve these two equations simultaneously. But since we do not have any further information or equations, we cannot determine the specific coordinates of point Y.
To find the coordinates of point Y, we can 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:
Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)
In this case, we know that the midpoint is (3,4), and we want to find the coordinates of point Y.
Let's assign the coordinates of Y as (x, y). Using the midpoint formula:
Midpoint = ((x₁ + x)/2, (y₁ + y)/2)
Plugging in the values of the midpoint (3,4):
(3,4) = ((x₁ + x)/2, (y₁ + y)/2)
Now, comparing the coordinates individually:
3 = (x₁ + x)/2
4 = (y₁ + y)/2
To find the value of x, we can rearrange the first equation:
6 = x₁ + x
x = 6 - x₁
Similarly, to find the value of y, we can rearrange the second equation:
8 = y₁ + y
y = 8 - y₁
Since we don't know the values of x₁ and y₁, we cannot determine the exact coordinates of point Y without additional information.