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.

• i) State the coordinates of the centre of the circle described by each equation below.
• ii) State the radius and the x— and y-intercepts of the circle.
• iii) Sketch a graph of the circle.

\displaystyle x^2 + y^2 = 169

• i) State the coordinates of the centre of the circle described by each equation below.
• ii) State the radius and the x— and y-intercepts of the circle.
• iii) Sketch a graph of the circle.

\displaystyle x^2 + y^2 = 2.89

• i) State the coordinates of the centre of the circle described by each equation below.
• ii) State the radius and the x— and y-intercepts of the circle.
• iii) Sketch a graph of the circle.

\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.