20.09 Distance from a point to a line (Extended)
Write down the formula to find the perpendicular distance d from the point \left(x_1, y_1\right) to the line A x + B y + C = 0.
Find the perpendicular distance from the following points to the given line:
Point \left(0,0\right), Line : 4 x + 7 y + 5 = 0
Point \left(- 9,-3\right), Line : 6 x + 3 y + 1 = 0
Point \left(3, 5\right), Line : 4 x + 3 y + 1 = 0
Point \left(4, - 3 \right), Line : 24 x + 7 y - 3 = 0
Point \left(5, 4\right), Line : 5 x - 12 y = 0
Point \left( - 5 , 3\right), Line : 3 x - 2 y - 5 = 0
Find the perpendicular distance from the point (8, 7) to the line 9 x - 9 y - 0 = 0.
Find the value of k with the following conditions:
The perpendicular distance from the point \left(- 5,-1\right) to the line - 2 x - 7 y + k = 0 is \dfrac{10}{\sqrt{53}}.
The perpendicular distance from the point (\left(6,k\right), to the line 6 x + \left( - 2 y\right) + \left( - 6 \right) = 0 is \dfrac{40}{\sqrt{40}}.
Consider the lines L_{1}: x + 2 y + 5 = 0 and L_{2}: x + b y + 20 = 0.
Find the distance between L_{1} and the origin.
Solve for the value(s) of b such that L_{1} is twice as far from the origin as L_{2}.
Consider the circle represented by the equation x^{2} + y^{2} = 0.81.
Find the centre of the circle.
Find the radius of the circle.
Find the perpendicular distance from the origin to the line - 4 x + \left( - 7 y\right) + 8 = 0.
State the number of intersections between the line and circle. Explain your answer.
Consider the circle represented by the equation \left(x - \left( - 3 \right)\right)^{2} + \left(y - \left( - 2 \right)\right)^{2} = 4.
Find the centre of the circle.
Find the radius of the circle.
Find the perpendicular distance from the centre of the circle to the line - 3 x + 5 y + \left( - 5 \right) = 0.
State the number of intersections between the line and circle. Explain your answer.
The three points A(- 3, - 4), B(0, - 10) and C(- 6, - 7) form a triangle.
Find the gradient of the line AC.
Find the equation of the line AC in general form.
Find the midpoint, D, of the line AC.
Find the gradient of the line BD.
Is BD perpendicular to AC?
What type of triangle is ABC?
Find the length of the line BD. Give your answer in simplest surd form.
Find the length of the line AC. Give your answer in simplest surd form.
Find the area of triangle ABC.
Find the coordinates of the point E that would make ABCE a parallelogram.
The points A \left(5, 7\right), B \left(9, 10\right), C \left(6, 4\right) and D \left(2, 1\right) are the vertices of a parallelogram.
Determine the equation of the line going through AB.
If AB is the length of the parallelogram, find the perpendicular height of the parallelogram.
Determine the exact area of the parallelogram.