Analytic Geometry Chapter Review
Chapter
Chapter 2
Section
Analytic Geometry Chapter Review
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Solutions 25 Videos

On the design plan for a garden, a straight path runs from (-25, 20) to (40, 36). A lamp is going to be placed at the midpoint of the path. Determine the coordinates for the lamp.

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0.00mins
Q1

\triangle ABC has vertices at A(-4, 4), B(-4, -2), and C(2, -2).

a. Determine the equation of the median from B to AC.

b. Is the median for part a) also an altitude? Explain how you know.

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2.02mins
Q2

\triangle LMN has vertices at L(O, 4), M(-5, 2), and N(2, -2). Determine the equation of the perpendicular bisector that passes through MN.

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1.59mins
Q3

Which point is closer to the origin: P(-24, 56) or Q(35, -43)?

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1.01mins
Q4

A builder needs to connect a partially built house to a temporary power supply. On the plan, the coordinates of the house are (20, 110) and the coordinates of the power supply are (105, 82). What is the least amount of cable needed?

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0.56mins
Q5

\triangle QRS has vertices at Q(2, 6), R(—3, 1), and 5(6, 2). Determine the perimeter of the triangle.

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2.13mins
Q6

\triangle XYZ as vertices at X(1, 6), Y(-3, 2), and Z(9, 4). Determine the length of the longest median in the triangle.

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2.33mins
Q7

a. Determine the equation of the circle that is centred at (0, 0) and passes through point (-8, 15).

b. Identify the coordinates of the intercepts and three other points on the circle.

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1.31mins
Q8

A circle has a diameter with endpoints C(20, -21) and D(-20, 21). Determine the equation of the circle.

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1.51mins
Q9

Determine the equation of this circle.

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0.16mins
Q10

The point (-2, k) lies on the circle x^2 + y^2 = 20. Determine the values of k. Show all the steps in your solution.

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0.50mins
Q11

\triangle ABC has vertices as shown. Use analytic geometry to categorize \triangle ABC. Show your work.

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1.03mins
Q12

A triangle has vertices at A(1, 1), B(-2, -1), and C(3, -2). Calculate the side lengths to determine whether the triangle is isosceles, equilateral, or scalene.

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1.12mins
Q13

Show that the quadrilateral with vertices at J(-1, 1), K6, 4), L(8, 4), and M(4, 1) is a rhombus. What is the length of the side?

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2.13mins
Q14

Determine the type of quadrilateral described by the vertices R(-3, 2), 5(- 1, 6), T(3, 5), and U(1, 1). Show all the steps in your solution.

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2.52mins
Q15

A quadrilateral has vertices at A(-3, 1), B(-5, -9), C(7, -1), and D(3, 3). The mid segments of the quadrilateral form ?

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2.07mins
Q16

Which of the points A(10, 10),B (-7, 3), and C(0, -14) lie on a circle with centre O(5, -2)? What is the radius of this circle?

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2.26mins
Q17

A triangle has vertices at P(-2, 7), Q(-4, 2), and R(6, -2).

a. Categorize \triangle PQR .

b. Show that the mid point of the hypotenuse is the same distance from each vertex. What is the distance?

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3.38mins
Q18

Show that points (6, 7) and (-9, 2) are the endpoints of a chord in a circle with centre (0, 0).

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3.03mins
Q19

Quadrilateral JKZM has vertices as shown. Show that the diagonals of the quadrilateral bisect each other by showing they share the midpoint. What is the mid point?

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1.35mins
Q20a

\triangle PQR has vertices at P(0, -2), Q(4, 4), and R(-4, 5). Use analytic geometry to determine the coordinates of the orthocentre (the point where the altitudes intersect).

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5.56mins
Q21

\triangle XYZ has vertices at X(0, 1), Y(6, -1), and Z(3, 6). Use analytic geometry to determine the coordinates of the centroid (the point where the medians intersect).

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1.41mins
Q22

A new lookout tower is going to be built so that it is the same distance from three ranger stations. If the stations are at A(-90, 28), B(0, -35), and C(125, 20) on a grid, determine the coordinates of the point where the new tower should be built.

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5.47mins
Q23

Predict the type of quadrilateral that is formed by the points of intersection of the lines 3x+y-4=0, 4x-5y+30=0, 4y = -3x -1, and -4x + 5y +10 = 0. Give reasons for your prediction. Verify that your prediction is correct by solving this problem.

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2.11mins
Q24

A builder wants to run a temporary line from the main power line to a point near his site office. On the site plan, the site office is at S(25, 18) and the main power line goes through points T(1, 5) and U(29, 12). Each unit represents 1 m.

a. At what point should the builder connect to the main power line?

b. What length of cable will the builder need?

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3.17mins
Q25