Perpendicular lines：練習問題

Find the gradient of a line perpendicular to the line with equation \(2y + 8x = 10\).

A line passes through the point \((0, 3)\) and is perpendicular to the line \(y = 2x - 5\). Find the equation of this line.

Points \(R\) and \(S\) have coordinates \((-4, 2)\) and \((2, 6)\) respectively. Find the equation of the perpendicular bisector of \(RS\) in the form \(ax + by = c\), where \(a, b, c\) are integers.

Line \(L_1\) has the equation \(y = \frac{1}{5}x + 2\). Find the gradient of line \(L_2\) if \(L_2\) is perpendicular to \(L_1\).

Find the equation of the line that passes through the origin \((0,0)\) and is perpendicular to the line passing through \((2, 5)\) and \((4, 9)\).

Calculate the gradient of a straight line that is perpendicular to the line passing through the points \(A(-2, 5)\) and \(B(4, 8)\).

Find the equation of the line which passes through the point \((4, -1)\) and is perpendicular to the line segment connecting \(P(0, 5)\) and \(Q(2, 1)\).

A line segment joins the points \(A(-1, 4)\) and \(B(5, 12)\).
Find the equation of the perpendicular bisector of the line segment \(AB\).
Give your answer in the form \(ax + by = c\), where \(a\), \(b\), and \(c\) are integers.

The line segment joining points P\((2, 3)\) and Q\((5, -1)\) forms part of line \(L_1\).
(a) Calculate the gradient of line \(L_1\).
(b) Determine the gradient of a line \(L_2\) that is perpendicular to \(L_1\).
(c) Find the equation of line \(L_2\) if it passes through the origin \((0, 0)\).

Consider points A\((1, 2)\) and B\((7, 10)\).
(a) Find the coordinates of the midpoint of AB.
(b) Find the equation of the perpendicular bisector of the line segment AB in the form \(y = mx + c\).
(c) Determine if the point P\((10, 2)\) lies on this perpendicular bisector. Show your working.