Question

The slopes of perpendicular line segments are three/ four fraction and d/two What is the value of d?

a.)-3/2
b.)3/2
c.)-8/3
d.)8/3

Answer 1

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
`\bf slope=\cfrac{a}{{{ b}}}\qquad negative\implies -\cfrac{a}{{{ b}}}\qquad reciprocal\implies - \cfrac{{{ b}}}{a}`

what the dickens does that mean?

well, it means that their product is
`\bf \cfrac{a}{b}\cdot \cfrac{-b}{a}\implies -1`

so... in this case, one has a slope of 3/4 and the other has a slope of d/2

thus
`\bf \cfrac{3}{4}\cdot \cfrac{d}{2}=-1\implies \cfrac{3\cdot d}{4\cdot 2}=-1\implies \cfrac{3d}{8}=-1 \\\\\\ \textit{now we cross-multiply} \\\\\\ 3d=-8\implies d=\cfrac{-8}{3}`