Find the end point of a line segment with a start point of (3,4) and a length of \(5\sqrt{2}\). The line segment is moving along a path that forms a 45 degree angle with the positive x-axis.

Step 1 ：Step 1: For a line segment moving at a 45 degree angle, the change in x and y coordinates are the same. We can use the length of the line segment to find this change. Since the length of the line segment is \(5\sqrt{2}\), the change in the x and y coordinates is 5.

Step 2 ：Step 2: We add this change to the x and y coordinates of the start point to find the end point. So, the new x coordinate is \(3 + 5 = 8\) and the new y coordinate is \(4 + 5 = 9\).