The line through the points \((-5,7)\) and \((2,9)\)\) is perpendicular to the line through the points \((8,12)\) and \((x,24)\). Find the value of \(x\).
Answer:
Let the points be \(A(-5,7)\), \(B(2,9)\), \(C(8,12)\) and \(D(x,26)\).
Let the slope of \(AB\) be \(m_1\) and the slope of \(CD\) be \(m_2\).
The slope of \(AB\), \(m_{1}\) \(=\) .
If two lines are perpendicular, then the product of their slopes \(m_{1} × m_{2} is .
Therefore, the value of \(x\) is .