Given ABCD is a square
AC= BD = 4 units
Ac= BD pass origin of (0,0)
Find coordinates of A B C D
To find the coordinates of the four vertices of the square ABCD, we need to consider the information given. We know that AC and BD are equal and measure 4 units. Additionally, we are told that AC and BD pass through the origin (0,0).
Since AC and BD pass through the origin, we can conclude that the midpoint of each of these lines will be at (0,0). This is because the midpoint of any line segment that passes through the origin will also be at the origin.
Now, let's determine the coordinates of the midpoint of AC and BD. The midpoint formula is given by:
Midpoint = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]
For AC:
- Let point A have coordinates (x₁, y₁)
- Let point C have coordinates (x₂, y₂)
- We know that the midpoint of AC is (0,0)
Substituting the known values, we have:
0 = (x₁ + x₂) / 2
0 = (y₁ + y₂) / 2
Thus, x₁ + x₂ = 0 and y₁ + y₂ = 0.
Since AC is a diagonal of the square, we also know that the coordinates of point A and point C will have the same magnitude but with opposite signs. Let's denote the magnitude as m:
x₁ = -m and x₂ = m
y₁ = -m and y₂ = m
Now, we can determine the coordinates of A, B, C, and D:
A(-m, -m)
B(-m, m)
C(m, m)
D(m, -m)
Therefore, the coordinates of the vertices of the square ABCD are:
A: (-m, -m)
B: (-m, m)
C: (m, m)
D: (m, -m)
Since we do not have a specific value for m, we cannot determine the exact coordinates but we know that the x and y coordinates of A, B, C, and D will be equal but with opposite signs.