Chapter Review Analytic Geometry
Chapter
Chapter 2
Section
Chapter Review Analytic Geometry
Solutions 35 Videos

Find the midpoint of the line segment.

Q1a

Find the midpoint of the line segment.

Q1b

Find the midpoint of two given points below.

Q1c

Find the midpoint of two given points below.

Q1d

Determine the midpoint of the line segment with endpoints J(3, -5) and K(-5, -6).

Q2a

Determine the midpoint of the line segment with endpoints L(4, 8) and N(4, -2).

Q2b

a) Draw the triangle with vertices P(-2, 5), Q(6, 5), and R(2, -7).

b) Determine the midpoint of each side of the triangle algebraically.

c) Join the midpoints to form a smaller triangle. Compare this triangle to the original triangle.

Q3

a) Draw the triangle with vertices T(-8, 6), U(2, 10), and W(4, -4).

b) Draw the median from vertex U. Then, find an equation for this median.

c) Draw the altitude from vertex T. Then, find an equation for this altitude.

d) Draw the right bisector of TU. Then, find an equation for this right bisector.

Q4

The midpoints of the sides of \triangle ABC are D(4, 1), E(-2, 3), and F(1, -4).

a) Plot the midpoints. Use this plot to estimate the coordinates of the vertices of \triangle ABC.

b) Use analytic geometry to calculate the coordinates of the vertices of \triangle ABC.

Q5

Find the length of the line segment \overline{AB} where A(3, 17), B(8, 5).

Q6a

Find the length of each line segment.

Q6b

Find the length of each line segment.

Q6c

Find the length of each line segment.

Q6d

Determine the length of the line segment defined by each pair of points.

J(4, 8) and K(4, -2)

Q7a

Determine the length of the line segment defined by each pair of points.

M(-3, -12) and N(-15, -7)

Q7b

Determine the length of the line segment defined by each pair of points.

P(-3, -2) and Q(5, 6)

Q7c

Determine the length of the line segment defined by each pair of points.

R(-1, 5) and S(4, -1)

Q7d

Determine the length of the line segment defined by each pair of points.

T(-2, 4) and U(7, 4)

Q7e

Determine the length of the line segment defined by each pair of points.

V(3, -5) and W(-5, -6)

Q7f

Determine the length of the median from vertex A of \triangle ABC.

Q8a

a) Draw the triangle with vertices D(5, 25), E(210,1), and F(3, 210).

b) Use analytic geometry to Classify \triangle DEF.

c) Determine the area of \triangle DEF.

Q9

Show that this triangle is isosceles.

Q10

A triangle has vertices D(-2, 7), E(-4, 2), and F(6, -2).

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.

Q11

A map shows a main gas pipeline running straight from A(45, 60) to B(65, 40).

a) How long is the section of pipeline from A to B if each unit on the map grid represents 1 km?

b) A branch pipeline runs perpendicular to the main pipeline and meets it at a point halfway between A and B. Find the coordinates of this point.

c) Is the point C(63, 54) on the branch pipeline? Explain your reasoning.

d) What is the shortest route for connecting point C to the main pipeline? Explain.

Q12

Find the shortest distance from the origin to the line defined by y = 3x - 10.

Q13

Determine the equation for the circle.

Q14a

Determine the equation for the circle.

Q14b

Determine the equation for the circle.

Q14c

Find an equation for the circle that is centred on the origin and has a radius of 4.5.

Q15a

Find an equation for the circle that is centred on the origin and ha a diameter of 14.

Q15b

Find an equation for the circle that is centred on the origin and has a radius of \sqrt{12}.

Q15c

Find an equation for the circle that is centred on the origin and passes through the point (4, 7).

Q15d

a) Determine whether the point A(-2, -6) lies on the circle defined by x^2 + y^2 = 40.

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

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

d) Use a graph to check your answers to parts a), b), and c).

e) Explain why A is the only point on the line that also lies on the circle.

Q16

a) Show that the line segment joining A(-3, 1) and B(1, 3) is a chord of the circle defined by x^2 + y^2 = 10

b) Determine an equation for the right bisector of the chord AB.

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

A communication tower can send and receive signals from cell phones up to 20 km away. A cell phone user is 15 km east and 13 km south of the tower. Is this user able to receive a signal from the tower?