Question

parallel and perpendicular lines. (tb p215)

• work in aleks and complete 30 minutes in each session.
• study lesson 3 - 8 \slope and equations of lines\ tb p215.
• solve the following exercises.

1. - qué linea, a o b, es perpendicular a la recta c?

la línea c pasa por los puntos (-3, 4) y (3, 6).
explicar tu respuesta.

Explanation:

Step1: Calculate the slope of line \(c\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For line \(c\) with points \((-3,4)\) and \((3,6)\), we have \(m_c=\frac{6 - 4}{3-(-3)}=\frac{2}{6}=\frac{1}{3}\)

Step2: Calculate the slope of line \(a\)

Using the points \((-2,1)\) and \((-1,-2)\) for line \(a\), \(m_a=\frac{-2 - 1}{-1-(-2)}=\frac{-3}{1}=- 3\)

Step3: Calculate the slope of line \(b\)

Using the points \((1,3)\) and \((2,-1)\) for line \(b\), \(m_b=\frac{-1 - 3}{2 - 1}=\frac{-4}{1}=-4\)

Step4: Check the perpendicular - slope relationship

Two lines are perpendicular if \(m_1\times m_2=-1\). Since \(m_c\times m_a=\frac{1}{3}\times(-3)=-1\)

Answer:

La línea \(a\) es perpendicular a la línea \(c\) porque el producto de sus pendientes \(m_c\times m_a=\frac{1}{3}\times(-3)=-1\)