slopes of perpendicular lines are NEGATIVE RECIPROCAL to each other
namely, if say one has a slope of a/b then the other will have a slope of [tex]\bf slope=\cfrac{a}{{{ b}}}\qquad negative\implies -\cfrac{a}{{{ b}}}\qquad reciprocal\implies - \cfrac{{{ b}}}{a}[/tex]
what the dickens does that mean?
well, it means that their product is [tex]\bf \cfrac{a}{b}\cdot \cfrac{-b}{a}\implies -1[/tex]
so... in this case, one has a slope of 3/4 and the other has a slope of d/2
thus [tex]\bf \cfrac{3}{4}\cdot \cfrac{d}{2}=-1\implies \cfrac{3\cdot d}{4\cdot 2}=-1\implies \cfrac{3d}{8}=-1
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\textit{now we cross-multiply}
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3d=-8\implies d=\cfrac{-8}{3}[/tex]
