Determine the coordinates of the midpoint of the line segment with the pair of endpoints.
\displaystyle
(-1, -2)
and \displaystyle
(-7, 10)
Determine the coordinates of the midpoint of the line segment with the pair of endpoints.
\displaystyle
(5, -1)
and \displaystyle
(-2, 9)
Determine the coordinates of the midpoint of the line segment with the pair of endpoints.
\displaystyle
(0, -4)
and \displaystyle
(0, 12)
Determine the coordinates of the midpoint of the line segment with the pair of endpoints.
\displaystyle
(6, 4)
and \displaystyle
(0, 0)
A diameter of a circle has endpoints A(9, -4)
and B(3, -2)
. Determine the centre of the circle.
Describe all the points that are the same distance from points A(-3, - 1)
and B(5, 3)
.
A hockey arena is going to be built to serve two rural towns.
On a plan of the area, the towns are
located at (1, 7)
and (8, 5)
.
If the arena needs to be the same distance from both towns, determine an equation to describe the possible locations for the arena.
\triangle
PQR has vertices at P(12, 4)
, Q(-6, 2)
, and R(-4, -2)
.
a) Determine the coordinates of the midpoints of its sides.
b) Determine the equation of the median from vertex Q
c) What is the equation of the perpendicular bisector of side PQ
?
Calculate the distance between the pair of points.
(2, 2) and (7, 4)
Calculate the distance between the pair of points.
(-3, 0) and (8, -5)
Calculate the distance between the pair of points.
(2, 9) and (-5, 9)
Calculate the distance between the pair of points.
(9, -3) and (12, -4)
A power line is going to be laid from A(-22, 15) to B(7, 33) to C(10, 18) to D(-1, 4). If the units are metres, what length will the power line be?
Determine the distance between point (-4, 4)
and the line y = 3x - 4
.
Show that \triangle ABC
has three unequal sides.
\displaystyle
x^2 + y^2 = 169
\displaystyle
x^2 + y^2 = 2.89
\displaystyle
x^2 + y^2 = 98
Determine the equation of a circle that has its centre at (0, 0) and passes through (-5, 0).
Determine the equation of a circle that has its centre at (0, 0) and passes through (0, 7).
Determine the equation of a circle that has its centre at (0, 0) and passes through (-3, -8).
Determine the equation of a circle that has its centre at (0, 0) and passes through (4, 9).
A raindrop falls into a puddle, creating a circular ripple. The radius of the ripple grows at a steady rate of 5 cm/s. If the origin is used as the location where the raindrop hits the puddle, determine the equation that models the ripple exactly 6 s after the raindrop hits the puddle.
Determine whether each point is on, inside, or outside the circle x^2 + y^2 = 45
. Explain your reasoning.
a) (6, -3)
b) (-1, 7)
c) (-3, 5)
d) (-7, -2)
A line segment has endpoints A(6, -7)
and B(2, 9)
.
a) Verify that the endpoints ofAB are on the circle with equation x^2 + y^2 = 85
.
b) Determine the equation of the perpendicular bisector of AB.