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Create a new UCS called with an origin at the intersection of gridlines 1 & J. The X axis should be perpendicular to grid line K and the Y axis aligned with the J gridline. Turn Ortho on and create a line from the intersection of the grid lines 1 & J to intersect with grid line A.
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It helps to draw a small circle around the intersection of the grid lines 1 and J. This saves having to constantly pan to see the grid line letters and numbers.
Type UCS and place the origin at the centre of your circle. Then in response to the command line's instruction, use the perpendicular osnap point on grid line K to place a point on the positive X axis. Then pick a point on the J axis to create a point on the positive Y axis of the UCS.
You can save this UCS for later use by typing UCS and using the name option.
Now turn ortho mode on (F8 function key). Draw a line from the intersection of J and 1 to cross grid line A.
Note that there is no accurate osnap point where the line crosses grid line A. So you have to draw the line past grid line A, then use the Trim command with grid line A as a cutting edge.
You can now measure the line with click and grip - properties on right mouse.