Question

the slope of the segment through (3, -2), and (0, 2) is -4/3. (type an integer or a simplified fraction.) find the slope of the segment through (-1, -5) and (3, -2). the slope of the segment through (-1, -5) and (3, -2) is 3/4. (type an integer or a simplified fraction.) find the product of the slopes of the two segments meeting at the point (-1, -5). the product of the slopes of the two segments meeting at the point (-1, -5) is -21/4. (type an integer or a simplified fraction.) find the product of the slopes of the two segments meeting at the point (0, 2). the product of the slopes of the two segments meeting at the point (0, 2) is

Explanation:

Step1: Calculate the slope between \((-1,-5)\) and \((3,-2)\)

Use the slope formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Here \(x_1=-1,y_1 = -5,x_2=3,y_2=-2\).
\(m_1=\frac{-2-(-5)}{3-(-1)}=\frac{-2 + 5}{3 + 1}=\frac{3}{4}\)

Step2: Calculate the slope between \((3,-2)\) and \((0,2)\)

Use the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Here \(x_1 = 3,y_1=-2,x_2=0,y_2 = 2\).
\(m_2=\frac{2-(-2)}{0 - 3}=\frac{2+2}{-3}=-\frac{4}{3}\)

Step3: Calculate the product of the slopes

Multiply \(m_1\) and \(m_2\).
\(m_1\times m_2=\frac{3}{4}\times(-\frac{4}{3})=- 1\)

Answer:

\(-1\)