11.17 Perpendicular lines (Extended)
Describe what it means for two lines to be perpendicular.
If two lines are perpendicular, state the product of their gradients.
State whether the following pairs of lines are perpendicular:
y = x + 1 and y = x - 1
y = 3 x - 7 and y = - 3 x + 6
y = - 3 x + 6 and y = \dfrac{x}{3} + 7
y = \dfrac{2 x}{3} + 4 and y = -1 - \dfrac{3 x}{2}
y = - \dfrac{x}{3} - 9 and y = - \left( 3 x - 27 \right)
y = 3 x - 5 and y = -\dfrac{1}{3} x + 6
y=-\dfrac{2x}{3}+1 and y=-1+\dfrac{3x}{2}
y=\dfrac{3x}{5}+6 and y=\dfrac{-5x-30}{-3}
Given that the following pairs of lines are perpendicular, calculate the value of m:
5 x + 4 y =-8 \\m x + 9 y = 8
- 6 x + 6 y = 8 \\ m x + 10 y =- 8
Find the gradient of the line perpendicular to the following lines:
Line with gradient 6
Consider the lines L_{1}: 8 x = - 7 y + 3 and L_2: 7 y - 8 x = 7.
Find the gradient of line L_{1}.
Find the gradient of line L_{2}.
Are the two lines perpendicular?
Find the equation of a line described by the following information:
Perpendicular to the x-axis and passes through \left( - 8 , - 1 \right).
Perpendicular to the y-axis and passes through \left( - 8 , - 8 \right).
Perpendicular to y = - \dfrac{x}{2} + 5, and goes through the point \left(0, 6\right).
Perpendicular to y = 6 x + 10, and has the same y-intercept.
Perpendicular to the line that passes through \left(1, 1\right) and \left(3, 13\right), and has a y-intercept of \left(0, - 4 \right).
The line L_{1} is perpendicular to y = 5 x - 4 and cuts the y-axis at 1.
Find the gradient of line L_{1}.
Find the equation of line L_{1}.
The line L_{1} is perpendicular to y = 10 x + 8 and passes through the point of intersection of the lines y = x + 5 and 8 x - 10 y =- 60 .
Find the gradient of line L_{1}.
Find the point of intersection of y = x + 5 and 8 x - 10 y + 60 = 0.
Find the equation of the perpendicular line L_{1}.
Consider the rhombus ABCD on the number plane:
Find the gradients of its diagonals.
Gradient of AC
Gradient of BD
Are the diagonals of the rhombus perpendicular? Explain your answer.
The four vertices of quadrilateral ABCD have been plotted on the number plane:
Find the gradient of the following sides:
AB
BC
DC
AD
Given that side AB = BC, determine the type of quadrilateral described by the four points.