Find the midpoint of each segment.

Find the midpoint of each segment.

Determine the midpoint of the line segment with endpoints P(—5, —8) and Q(3, 2).

Determine the midpoint of the line segment with endpoints X(—4, 3) and Y(7, —8).

a) Draw the triangle with vertices D(—3, 4), EU, —2), and F(5, 5).

b) Draw the median from vertex D. Then, find an equation in the form y = mx + b for this median.

c) Draw the right bisector of DF. Then find the equation in the form y = mx + b for this right bisector.

d) Draw the altitude from vertex F. Then, find an equation in the form y = mx + b for this altitude.

Find the length of each line segment.

Find the length of each line segment.

Determine the length of the line segment defined by each pair of points. Round answers to the nearest tenth of a unit.

A (-3,5) and B(4,2)

Determine the length of the line segment defined by each pair of points. Round answers to the nearest tenth of a unit.

M(-2,6) and Q(7,-3)

a) Determine the length of the median from vertex X of \triangle XYZ. Round your answer to the nearest tenth of a unit.

b) Show that \triangle XYZ is isosceles.

c) Determine the perimeter of the triangle. Round your answer to the nearest tenth of a unit.

d) Describe how to use geometry software to answer part c).

a) Show algebraically that this triangle is a right triangle.

b) Find the midpoint of the hypotenuse.

c) Show that this midpoint is equidistant from each of the vertices.

A section of a ski jump on a ski hill is shown as a straight line running from C(20, 35) to D(70, 85) on a map grid.

a) How long is the section of the ski jump if each unit on the map grid represents 1 m?

b) Is the point E(40, 55) on the ski jump? Explain your reasoning.

c) Is the point F(50, 35) on the ski jump? Explain your reasoning.

Determine an equation of each circle.

Determine an equation of each circle.

Determine an equation of each circle.

Find the equation for the circle that is centered on the origin and

a) has a radius of 5.2

b) has a radius of sqrt{18}

c) has a diameter of 20

d) passes through the point (-2,3)

Find the equation for the circle that is centered on the origin and passes through the point (-2,3)

a) Show that the line segment joining M(—4, —1) and N(4, 1) is a chord of the circle defined by x^2 + y^2 = 17.

b) Determine an equation of the right bisector of the chord MN.

c) Show that the line in part b) passes through the centre of the circle.

a) Determine whether the point D(—2, 5) lies on the circle defined by x^2 + y^2 = 29.

b) Find an equation for the radius from the origin O to point D.

c) Find an equation for the line that passes through D and is perpendicular to OD.