Distance between a point and a straight line

\(\bullet \; \) Find the distance between the point \((2, 3)\) and the line \(y = 4x + 1\).

\(\bullet \; \) Calculate the distance from the point \((-1, 5)\) to the line \(y = -2x + 3\).

\(\bullet \; \) Determine the distance between the point \((0, 0)\) and the line \(2x - 3y + 6 = 0\).

\(\bullet \; \) Find the shortest distance between the point \((1, 2)\) and the line \(y = 2x - 3\).

\(\bullet \; \) Calculate the distance from the point \((3, 4)\) to the line \(3x + 4y = 12\).

\(\bullet \; \) Determine the distance between the point \((1, -1)\) and the line \(y = x + 2\).

\(\bullet \; \) Find the distance from the point \((-2, 7)\) to the line \(2x + 3y - 8 = 0\).

\(\bullet \; \) Calculate the shortest distance between the point \((5, -2)\) and the line \(y = -3x + 1\).

\(\bullet \; \) Determine the distance between the point \((-3, 1)\) and the line \(4x - 2y = 10\).

\(\bullet \; \) Find the distance from the point \((0, 6)\) to the line \(5x + 12y = 24\).

ANSWERS

\(\bullet \; \displaystyle \frac{6}{\sqrt{17}}\).

\(\bullet \; \displaystyle 0\).

\(\bullet \; \displaystyle \frac{6}{\sqrt{13}}\).

\(\bullet \; \displaystyle \frac{3}{\sqrt{5}}\).

\(\bullet \; \displaystyle \frac{13}{5}\).

\(\bullet \; \displaystyle 2\sqrt{2}\).

\(\bullet \; \displaystyle \frac{9}{\sqrt{13}}\).

\(\bullet \; \displaystyle \frac{6}{5}\sqrt{10}\).

\(\bullet \; \displaystyle \frac{12\sqrt{5}}{5}\).

\(\bullet \; \displaystyle \frac{48}{13}\).