Line u passes through points (8, 7) and (2, 14). Line v is perpendicular to u. What is the slope of line v?
Question
Line u passes through points (8, 7) and (2, 14). Line v is perpendicular to u. What is the slope of line v?
Solution
To find the slope of line v, we first need to find the slope of line u. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula (y2 - y1) / (x2 - x1).
Step 1: Find the slope of line u The slope of line u (m_u) passing through points (8, 7) and (2, 14) is given by: m_u = (14 - 7) / (2 - 8) = 7 / -6 = -7/6
Step 2: Find the slope of line v The slope of a line v that is perpendicular to another line with slope m is given by the negative reciprocal of m. Therefore, the slope of line v (m_v) is: m_v = -1 / m_u = -1 / (-7/6) = 6/7
So, the slope of line v is 6/7.
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