QuestionIf a green line has a slope of $\frac{3}{4}$ , what is the slope of the perpendicular red line?

Studdy Solution

STEP 1

Assumptions1. The green line has a slope of $\frac{3}{4}$ . The red line is perpendicular to the green line

STEP 2

In geometry, the slopes of two lines that are perpendicular to each other are negative reciprocals of each other. This means that the slope of the red line is the negative reciprocal of the slope of the green line.
The formula to find the negative reciprocal of a number is $Negative\, reciprocal = -\frac{1}{number}$

STEP 3

Now, plug in the given value for the slope of the green line to calculate the slope of the red line.
$lope_{red} = -\frac{1}{lope_{green}}$

STEP 4

Substitute the value of the slope of the green line into the equation.
$lope_{red} = -\frac{1}{\frac{3}{4}}$

STEP 5

Calculate the slope of the red line.
$lope_{red} = -\frac{1}{\frac{3}{4}} = -\frac{4}{3}$ Therefore, the slope of the red line is $-\frac{4}{3}$ .

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