former

What is important is the shape of the curve connecting the 2 CPs, it’s not straight. We are using the 2 CPs to deduce a point lying on that curve. Linear extrapolation only give an estimate not the exact stddev. Like I said before, we can use the weights and covariance matrix to calculate the exact value but it’s unyieldy, not going to be asked on the exam. You can do it easily with excel though.
just draw a chart, x axis is stddev, y is return. Draw a horizontal line at the level of return required, it will cut the actual curve at a lower x than that of the straight line connecting 2 CPs.