Geometri Ruang: Konsep Dimensi Tiga

Hello everyone! Today we are studying Three Dimensional Geometry, focusing specifically on finding the distance from a point to a line.

Given a cube A B C D E F G H with a side length of six centimeters, what is the distance from point H to line A C? We have five options shown here.

Let us label the vertices A through H. For our analysis, note that A C, H A, and H C are face diagonals. Using the formula side length times the square root of two, each diagonal measures six square root of two centimeters, making triangle H A C an equilateral triangle.

Let O be the midpoint of line A C. The distance from H to A C is line H O. By calculation, H O equals the square root of H A squared minus A O squared. This gives us the square root of seventy-two minus eighteen, which is the square root of fifty-four, simplifying to three square root of six.

The final result is three square root of six centimeters. Therefore, the correct answer is option A.

And there is our final answer. Great work!