13.16 Distance
Find the length of each vertical interval on the number planes:
A \left(2, 5\right) and B \left(2, 8\right)
A \left(-7, -1\right) and B \left(-7, -6\right)
A \left(4, - 5 \right) and B \left(4, 5\right)
A \left( - 2 , 2\right) and B \left( - 2 , - 3 \right)
Find the length of each horizontal interval on the number planes:
A \left(3, 2\right) and B \left(9, 2\right)
A \left( - 4 , 5\right) and B \left( - 7 , 5\right)
A \left( - 5 , - 4 \right) and B \left(9, - 4 \right)
A \left( 3 , - 1 \right) and B \left(-5, - 1 \right)
For each of the following right-angled triangles, find the length of side AC. Round your answer to two decimal places if necessary.
For each of the following right-angled triangles:
Find the length of interval PQ.
Find the length of interval QR.
Find the length of PR, rounding to two decimal places if necessary.
P \left( - 6 , 5\right), Q \left( - 6 , 2\right) and R \left( - 2 , 2\right)
P \left( - 1 , 9\right), Q \left( - 1 , 6\right) and R \left( - 5 , 6\right)
P \left( - 4 , 6\right), Q \left( - 4 , 2\right) and R \left(3, 2\right)
P \left( - 3 , - 6 \right), Q \left( - 3 , - 1 \right) and R \left(1, - 1 \right)
For each of the following right-angled triangles:
Find the length of interval AB.
Find the length of interval BC.
Find the length of AC denoted by c, rounding to two decimal places if necessary.
A \left( - 2 , 4\right), B \left( - 2 , - 1 \right) and C \left( - 14 , - 1 \right)
A \left( - 2 , 7\right), B \left( - 2 , - 4 \right) and C \left(5, - 4 \right)
Find the length of AB shown on the graph. Round your answer to two decimal places.
Find the distance of the given point P from the origin.
P \left(12, 16\right)
P \left( - 12 , 16\right)
P \left(7, 11\right)
P \left( - 5 , - 4 \right)
For each of the following graphs, find the length of the interval AC. Round your answer to two decimal places if necessary:
Find the distance between Point A and Point B. Write your answer in surd form if necessary.
A \left(1, 4\right) and B \left(7, 12\right)
A \left(4, 2\right) and B \left( - 8 , - 7 \right)
A \left( - 1 , 9\right) and B \left( - 4 , 1\right)
A \left(-1, - \dfrac{3}{5} \right) and B \left(4, \dfrac{12}{5}\right)
Consider the points M \left( - 9 , - 1 \right) and N \left(1, 5\right).
Find the exact distance from M to the origin.
Find the exact distance from N to the origin.
Which point is closer to the origin?
Given P \left(4, 3\right), M \left( - 3 , - 4 \right) and N \left( - 7 , 1\right).
Find the distance from P to M to two decimal places.
Find the distance from P to N to two decimal places.
Which point is further from P?
Consider the Points A \left(12, 3\right) and B \left(14, 0\right).
Find the length of AB to two decimal places.
If M is the midpoint of AB, find the length of AM to two decimal places.
AM is a vertical interval 3 units long. If A is the point \left( - 2 , 6\right), find two possible coordinates of M.
Consider the points A \left( - 2 , - 6 \right), B \left(4, - 2 \right) and C \left(1, - 4 \right). Find:
The exact distance AC.
The exact distance BC.
What do you notice about the distance between the points?
K is the midpoint of A \left(3, 1\right) and C \left(15, - 7 \right). Find the distance from A to K correct to one decimal place.
A triangle is formed by three points:A \left(4, - 3 \right), B\left(1, 0\right) and C \left(7, 0\right). Find the following:
The distance BC.
The exact distance AB.
The exact distance AC.
Is this triangle equilateral, isosceles or scalene?
ABCD is a rhombus whose vertices are A \left(1, 2\right), B \left(3, 10\right), C \left(11, 12\right) and D \left(9, 4\right). Find:
The exact length of diagonals:
AC
BD
The exact area of the rhombus.
A circle with centre at point C \left(3, 4\right) has point A \left( - 12 , 12\right) lying on its circumference. Find:
The radius of the circle.
The exact circumference of the circle.
The distance between point \left(20, 4\right) and the centre.
Does the circle also pass through the point \left(20, 4\right)? Explain your answer.
A triangle has vertices at A \left(1, - 1 \right), B \left( - 3 , - 4 \right) and C \left(5, - 4 \right).
Find the length of the following sides:
AB
AC
BC
Is this triangle equilateral, isosceles or scalene?
Consider the triangle whose vertices are A \left(9, - 2 \right), B \left(2, - 8 \right) and C \left(3, 5\right).
How can we show that the triangle has a 90 \degree and two 45 \degree angles?
Find the length of the following sides in exact form:
AB
AC
BC
Does the triangle have a 90 \degree and two 45 \degree angles?
\triangle PQR has vertices P \left(2, - 6 \right), \, Q \left( - 9 , - 17 \right) and R \left( - 5 , 1\right).
Find the length of the following sides in exact form:
PQ
QR
PR
Is the triangle right-angled?
The points M \left( - 3 , - 5 \right) and R \left(4, - 12 \right) are the end points of an interval. N \left( - 1 , - 7 \right) is a point on this interval.
Find the exact distance between the following points:
M and N
N and R
In what ratio does N divide MR?
Find the perimeter of the parallelogram whose vertices are A \left(3, 2\right), B \left( - 2 , 7\right), C \left(2, 9\right) and D \left(7, 4\right). Round your answer correct to one decimal place.
The isosceles \triangle PQR is shown on the number plane:
Find the area of the triangle.
Find the exact length of PR.
Find the exact value of d, the perpendicular distance from Q to the side PR.
Consider the points P \left( 10 x, - 6 x\right) and Q \left( 4 x, 2 x\right), where x > 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.
P \left(- 4, - 4 \right), Q \left(5, - 7 \right), R \left(9 , - 11\right) and S \left(0, - 8\right) are the vertices of a quadrilateral.
Find the exact length of side PQ.
Find the exact length of side QR.
Find the exact length of side RS.
Find the exact length of side SP.
Find the exact length of the diagonal PR.
Find the exact length of the diagonal QS.
Classify the quadrilateral.