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A(1,2), B(4,0), C(k,2), D(1,-3). (answer given is k=-3/2)

If two lines are perpendicular the product of their slopes is -1.

The slope of AB is [tex]\frac{0-2}{4-1}[/tex] = [tex]\frac{-2}{3}[/tex]

The slope of CD is [tex]\frac{-3-2}{1-k}[/tex] = [tex]\frac{-5}{1-k}[/tex]

I set the product of these slopes equal to -1 and solve for k.

[tex]\frac{-2}{3}[/tex] x [tex]\frac{-5}{1-k}[/tex]=-1

10=3(k-1)

10=3k-3

13=3k

13/3=k

This is not the answer given and I am not seeing my error. Any help would be appreciated.

Latex question. The = sign and x symbol don't line up well with the rest of the equations in the first half of my post. How can I correct that?