Question

11 multiple choice 5 points what is the slope of a line that is perpendicular to the line shown on the graph? -4 -\frac{1}{4} \frac{1}{4} 4 12 multiple choice 5 points find the coordinates of the mid - point of the segment whose endpoints are h(8,2) and k(6,10). (14,12) (1,4) (7,6) (2,8)

Explanation:

Step1: Find the slope of the given line

Pick two points on the line, say \((0, 2)\) and \((4, 1)\). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). So \(m_1=\frac{1 - 2}{4-0}=-\frac{1}{4}\).

Step2: Use the perpendicular - slope relationship

If two lines are perpendicular, the product of their slopes is \(- 1\), i.e., \(m_1\times m_2=-1\). Given \(m_1 =-\frac{1}{4}\), then \(-\frac{1}{4}\times m_2=-1\). Solving for \(m_2\), we get \(m_2 = 4\).

Step3: Find the mid - point of the segment with endpoints \(H(8,2)\) and \(K(6,10)\)

The mid - point formula for two points \((x_1,y_1)\) and \((x_2,y_2)\) is \((\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). Here \(x_1 = 8,y_1 = 2,x_2 = 6,y_2 = 10\). So the mid - point is \((\frac{8 + 6}{2},\frac{2+10}{2})=(7,6)\).

Answer:

1. D. 4
2. C. \((7,6)\)