The cube above has edges of length 2 inches, and X and Y are midpoints of two of the edges.What is the distance, in inches, from point X to point Y? sqrt (2) 2 sqrt (6) 2sqrt (2)

To find the distance from point \(X\) to point \(Y\), we need to understand the positions of these points on the cube. Since \(X\) and \(Y\) are midpoints of two of the edges of the cube, we can infer that the line segment connecting \(X\) to \(Y\) will form the diagonal of one of the faces of the cube.Let's go through the steps to find the distance:Step 1: Identify the dimensions of the face that contains points \(X\) and \(Y\).Since the cube has edges of length 2 inches, the face that contains \(X\) and \(Y\) will also have dimensions of 2 inches by 2 inches.Step 2: Use the Pythagorean theorem to find the length of the diagonal.The diagonal of a rectangle can be found using the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.If we let \(d\) be the length of the diagonal, and since each side of the face is 2 inches, we have:\(d^2 = 2^2 + 2^2\)Step 3: Calculate the diagonal.\(d^2 = 4 + 4\)\(d^2 = 8\)Step 4: Take the square root to find \(d\).\(d = \sqrt{8}\)\(d = \sqrt{4 \cdot 2}\)\(d = 2 \sqrt{2}\)Answer:The distance from point \(X\) to point \(Y\) is \(2 \sqrt{2}\) inches.