Question

nombre _ periodo _ fecha _ parallel and perpendicular lines. (tb p.215) exercises 1.- di si las líneas a través de los puntos dados son paralelas. justifica tu respuesta. line 1: (2, 0), (-2, 2) line 2: (1, -2), (4, 4)

Explanation:

Step1: Calculate the slope of Line 1

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For Line 1 with points \((x_1,y_1)=(2,0)\) and \((x_2,y_2)=(-2,2)\), we have \(m_1=\frac{2 - 0}{-2 - 2}=\frac{2}{-4}=-\frac{1}{2}\)

Step2: Calculate the slope of Line 2

For Line 2 with points \((x_1,y_1)=(1,-2)\) and \((x_2,y_2)=(4,4)\), using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\), we get \(m_2=\frac{4-(-2)}{4 - 1}=\frac{4 + 2}{3}=\frac{6}{3}=2\)

Step3: Compare the slopes

Parallel lines have equal slopes. Since \(m_1=-\frac{1}{2}\) and \(m_2 = 2\), and \(-\frac{1}{2}
eq2\)

Answer:

The lines are not parallel.