Question

question 1 (multiple choice worth 4 points) (04.02 mc) a city planner is rerouting traffic in order to work on a stretch of road. the equation of the path of the old route can be described as y = 2/5 x - 4. what should the equation of the new route be if it is to be perpendicular to the old route and will go through point (q, p)? question 2 (multiple choice worth 4 points) (04.01 lc) if triangle abc is classified as a right triangle, which statement is true? o all three angles of triangle abc are congruent. o two sides of triangle abc are opposite reciprocals. o all three sides of triangle abc are congruent. o two sides of triangle abc are congruent. question 3 (multiple choice worth 4 points)

Explanation:

Step1: Find the slope of the new route

The equation of the old route is \(y = \frac{2}{5}x - 4\), so its slope \(m_1=\frac{2}{5}\).
If two lines are perpendicular, the product of their slopes is \(- 1\). Let the slope of the new route be \(m_2\). Then \(m_1\times m_2=-1\), so \(\frac{2}{5}\times m_2 = - 1\), and \(m_2=-\frac{5}{2}\).

Step2: Use the point - slope form

The point - slope form of a line is \(y - y_1=m(x - x_1)\), where \((x_1,y_1)=(p,q)\) and \(m =-\frac{5}{2}\).
Substituting into the formula, we get \(y - q=-\frac{5}{2}(x - p)\).

Answer:

\(y - q=-\frac{5}{2}(x - p)\)