Find the coordinates of the midpoint of the interval joining:
A line has a gradient of \dfrac{3}{10} and passes through the midpoint of A \left( - 6 , - 6 \right) and B \left(8, 8\right).
Find the coordinates of the midpoint of AB.
Find the equation of the line in general form.
Find the midpoint of \left( 2 m, 5 n\right) and \left( 6 m, n\right).
Find the coordinates of point B in each of the following:
Point M (1, 8) is the midpoint of A (2, 5) and B (x, y).
Point M (5, 6) is the midpoint of A (5, -2) and B (x, y).
Point M (4, -1) is the midpoint of A (10, -1) and B (x, y).
Consider the equations below:
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Equation 1: 0 = - 3 y - 5 x + 6
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Equation 2: y = mx - 1
If the line formed by Equation 1 is parallel to the line formed by Equation 2, find the gradient of Equation 2.
Find the equation of the line that is parallel to y = - 2 x + 9 and passes through the point \left( - 3 , 1\right).
Are the lines y = 7 x - 5 \text{ and } y = - 7 x + 6 perpendicular?
Given that the following two lines are parallel, find the value of d:
- x + 4 y + 2 = 0 \text{ and }d x + 12 y + 6 = 0Given that the following lines are perpendicular, find the value of t:
y = \left(t + 7\right) x - 1 \text{ and } y = \dfrac{x}{4} - 4What is the gradient of the line perpendicular to y = - \dfrac{x}{2} - 6 ?
State whether the following lines are perpendicular to y = 4 x + 5:
Consider the line L with equation 2 x + 5 y - 5 = 0 and point A\left( - 2 , - 3 \right).
Find the gradient, m, of a line that is perpendicular to L.
Write the equation of the line perpendicular to L that passes through point A in general form.
Consider the points A\left(5, 6\right) and B\left( - 13 , - 22 \right).
Find the gradient of the interval AB.
Find the midpoint of AB.
Find the equation of the perpendicular bisector of AB.
Find the equation of any lines that are both:
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parallel to x = - 2, and
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4 units away from the line x = - 2.
A line, L_{1}, is perpendicular to y = 9 x + 7 and passes through the point of intersection of the lines y = 3 x - 7 and 9 x - 4 y - 10 = 0.
Find the equation of the line L_{1}.
The points PQRST lie on a straight line such that PQ, QR, RS and ST are equidistant. Find the points Q ,R and S given P \left( - 4 , - 2 \right) and T \left( - 12 , 10\right).
Consider the interval AB that has been graphed on the number plane.
Copy the graph and add the intervals AC and BC such that ABC forms a right-angled triangle with the right angle at C, and such that C is to the right of AB.
Use Pythagoras’ theorem to find the length of interval AB. Leave your answer in exact (surd) form.
Which point is further from P \left(5, - 1 \right): M \left(10, - 6 \right) or N \left(1, 2\right)?
Find the exact distance from A \left(-1, - \dfrac{3}{5} \right) to B \left(4, \dfrac{12}{5}\right). Write your answer in exact (surd) form.
The graph shows a straight line that approximates the global life expectancy of a child over a period of one hundred years. The graph shows the life expectancy to be 53 years in 1910, and 69 years in 2010.
Use the midpoint formula to estimate the life expectancy of a child in 1960.
The table shows the number of smartphone users in a particular city.
Use the midpoint formula to estimate the number of smartphone users in 2009.
Use the midpoint formula to estimate the number of smartphone users in 2013.
| Year | Number of smartphone users |
|---|---|
| 2007 | 157\,904 |
| 2011 | 238\,502 |
| 2015 | 298\,080 |
Consider the points P \left( 10 x, - 6 x\right) and Q \left( 4 x, 2 x\right), where x \gt 0.
Find the distance between P and Q in terms of x.
Find the coordinates of the midpoint of the segment PQ in terms of x.
A circle with centre at point C \left( - 1 , 3\right) has point A \left( - 4 , - 1 \right) lying on its circumference.
Find the radius of the circle.
Find the exact circumference of the circle.
Find the distance between point \left( - 1 , 8\right) and the centre.
Does the circle also pass through the point \left( - 1 , 8\right)?
A triangle has vertices at A \left(4, - 4 \right), B \left( - 4 , 4\right) and C \left(12, 4\right).
Find the length of AB in exact form.
Find the length of AC in exact form.
Find the length of BC in exact form.
Is the triangle right-angled?
Is the triangle right-angled and isosceles?
Consider the points A \left( - 10, 10\right) and B \left( 16, 4\right).
Find the midpoint of AB.
For what value of k will the line y = 6 x + k bisect the interval AB?
Two cars have just left a car yard. One car heads south at 60\text{ km/h}, while the other heads west at 80\text{ km/h}.
Form an expression for the distance between the cars after t\text{ hours}.
At 5 pm, a prisoner broke out of an outback jail and headed east in a stolen vehicle at 120\text{ km/h}. An off duty prison officer, who was 250\text{ km} north of the prison, was immediately alerted and started rushing towards the prison at 75\text{ km/h}.
How far away from the escaped prisoner was the prison officer at 7 pm?