Here's more bells & whistles. The command plots:-textplot can be used to place formatted, rotated, colored text directly in the plot. This might be what you meant by "add bullet points to this plot". So here's the same plot with annotations of the 4 objects.

L:= y = -3/2*x + 2: Pt:= [2,1]:
m:= -1/implicitdiff(L, y, x):
Lperp:= y = m*(x-Pt[1]) + Pt[2]:
PtInt:= eval([x,y], solve({L, Lperp})):
plots:-display(
    plot(
        #Options specific to plotted objects:
        [rhs(L), rhs(Lperp), [PtInt], [Pt]], 
        x= -5..5, view= [-5..5, -5..5],
        style= [line$2, point$2], color= [red, "DarkGreen", black, red],
        symbolsize= 18, symbol= [solidcircle, soliddiamond],
        thickness= 0, 
        legend= [
            typeset(L, `\t`), 
            typeset(Lperp, ` `, `#mo(⊥)`,`\t`),
            typeset(`\n`, PtInt, `\n\t\t`),
            Pt
        ],
        #options specific to axes:
        labels= [x,y],
        axesfont= [Helvetica, Bold, 10],
        #options for whole plot: 
        caption= "\nExample 7: The given information is in red.", 
        captionfont= [Times, 18],
        title= "Perpendicular Lines\n", titlefont= [Helvetica, Bold],
        legendstyle= [location= bottom, font= [Times, Bold, 14]],
        scaling= constrained, size= [900$2]
    ),
    plots:-textplot(
        [
            [
                Pt[1]+.6, Pt[2]+1, 
                typeset(`#mo(⊥)`, ` `, Lperp), 
                rotation= arctan(m), 
                align= {above, right}, color= "DarkGreen"
            ],
            [Pt[], typeset(`  `, Pt), align= right, color= red],
            [
                PtInt[], typeset(`     `, PtInt), align= right, 
                font= [Times, Bold, 10]
            ],
            [
                -2, eval(rhs(L), x= -2) - 1, typeset(L), color= red,
                rotation= arctan(-1/m)
            ]
        ],
        font= [Times, Bold, 14]      
    )
);

@mmcdara I wouldn't consider these usages of & to be neutral operators. These symbols have no meaning to the kernel as operators, whereas &*, etc., do. But an appropriate help page for this would be ?symbol, and a link to that should appear on ?&.

@permanoon123 You'll learn much better by typing it in yourself.

I have a feeling that your mathematical abilities are at a significantly higher level than the book that you're using. What grade are you in, and what math, statistics, or computer science courses are you currently taking in school?

@Kitonum I should've used realcons instead of numeric to catch symbolic constants like your Pi:

plots:-display(
    [seq](
        plot3d(0, op([1,2],j), op(2,j)),
        j= indets(J, Int(Int(algebraic, name= range(algebraic)), name= range(realcons)))
    ),
    orientation= [180, 0, 180]
);

Now this will handle your most-recent case as well as the earlier VectorCalculus cases.

I'll admit that there was no good reason for me to use numeric; it was just my mistake.

@Kitonum My method is only intended for VectorCalculus:-int integrals in rectangular coordinates, not for integrals "written in the usual way". Obviously you can see how it can be modified to handle the case that you present.

@Kitonum Thank you for bringing this situation to my attention. The following plotting command will handle such cases as well as the original case:

plots:-display(
    [seq](
        plot3d(0, op([1,2],j), op(2,j)),
        j= indets(J, Int(Int(algebraic, name= range(algebraic)), name= range(numeric)))
    ),
    orientation= [180, 0, 180]
);

@JanBSDenmark You can force use of real branches with the RealDomain package. You can also include x > 0 in the solve command:

solve({f(x) = 5., x > 0})

@Jjjones98 The notation Diraderivatrc(n,t) is described on the ?Dirac help page. It's a generalized derivative of Dirac(t).

@dharr The return values of Eigenvectors are a vector and matrix (both types of rtable). When nops is used on an rtable, it does not tell you the number of elements! Indeed, the result is usually 3. The command for the number of elements of an rtable is numelems. There were 4 eigenvalues and eigenvectors for both the cases that you reported as having 3. Since the eigenvectors are returned as a matrix, they can't be counted with numelems either. You need to count the nonzero columns of the matrix.

The command Eigenvalues works on all these examples, so there's no need to find the eigenvalues "the hard way". The problem only occurs when computing the eigenvectors.

@acer You wrote: 

• I'm also waiting for the world's infatuation with thin clients and the cloud to end.

This may not be what you meant by "the cloud", but I don't think that people will ever grow tired of being able to access their documents from nearly any computer/phone in the world.

A related question is What kind of symmetry, if any, is necessarily possessed by a quadrilateral that has both an inscribed circle and a circumscribed circle? Even something as symmetric as a nonsquare rectangle doesn't have an inscribed circle, so I'd guess that such quadrilaterals are quite rare.

The error message comes from lines 189-193 of 

showstat(LinearAlgebra:-LA_Main:-Eigenvectors)

when the computed dimension of the null space associated with a particular eigenvalue (aka the geometric multiplicity) is higher than was expected (i.e., the algebraic multiplicity). I suspect that this error can only happen when there are parameters.

@mmcdara Can you show that 3D error that you described? My 3D plot below has all tickmarks on all three axes modified without any problem.

@Kitonum A variation of that that works in 1D input is

'`>=`'(a, b) 

(That's single forward quotes (aka unevaluation quotes) on the outside and single backward quotes (aka name quotes) on the inside.) The prettyprinted output is in the standard infix form, without any quotes.