Final answer:
To draw the square ABCD, calculate the distance between A and C to determine the side length, then find the coordinates of B and D and sketch the square by connecting the vertices.
Step-by-step explanation:
To draw a square with opposite vertices at A(2,-4) and C(10,4), we first determine the length of the side of the square. The distance between two points (x1, y1) and (x2, y2) in a coordinate plane is given by the formula: √[(x2 - x1)² + (y2 - y1)²]. Applying this formula to our points A and C, we find:
Distance AC = √[(10 - 2)² + (4 - (-4))²] = √[8² + 8²] = 8√2
Since AC is a diagonal of the square and we know that in a square the diagonal is √2 times a side, the side of the square (s) is:
s = AC / √2 = (8√2) / √2 = 8 units
Now that we have the side length, we can use it to determine the coordinates of the remaining vertices. The square will have vertices B and D such that B is 8 units to the right of A and D is 8 units above A. Thus, B will have coordinates (2 + 8, -4) = (10, -4) and D will have coordinates (2, -4 + 8) = (2, 4).
Finally, we sketch the square by drawing lines to connect vertices A to B, B to C, C to D, and D back to A.