Algebra/Chapter 17/Exercises

A set of exercises related to concepts from Chapter 17.

This set contains 18 exercises (including the Conceptual Questions)

Practice Problems

Section 17.1

17.1 (Using the Distance Formula) A is at (0, -2) and B is at (-5, -1). Find the distance between points A and B.

17.2 (Perimeter) Find the perimeter of the triangle PQR.

17.3 (Equidistant Point) A is at (4,4) and B is at (1,-1). P is a point on the x-axis that is equidistant from points A and B. What are the coordinates of point P?

Section 17.2

17.4 (Equidistance) Find the locus of points $P$ such that $P$ is equidistant from $(5,-1)$ and $(3,-8)$.

17.5 (Ambulance Station) Two hospitals are located at the points (5, -1) and (2, 8). An ambulance station is to be built such that it is equidistant from the two hospitals. Determine the locus of points that are equidistant from the two hospitals.

17.6 (Locus of a Circle)

1. Verify that the points $(-3,4)$ and $(4,3)$ lie on the circle $x^{2}+y^{2}=25$.
2. Determine the locus of points equidistant from the points $(-3,4)$ and $(4,3)$.
3. Determine the relationship between the center of the circle and the locus of points equidistant from the points $(-3,4)$ and $(4,3)$.

17.7 (The Rod) A rod of lenth $l$ slides with its ends on the x-axis and y-axis. Find the locus of its midpoint.

Answer to Problem 4

$4x^{2}+4y^{2}=l^{2}$

17.8 (The Third Vertex) Two verticies of of a triangle are at $(-3,5)$ and $(1,2)$. Find the locus of the third vertex, such that the area of the triangle is 10 square units.

17.9 (Locus from Ordered Pairs) Sketch the set of ordered pairs. Then write an equation for a locus that all of the points in each set might satisfy.

1. $\{(-5,0),(5,0),(0,-5),(0,5)\}$
2. $\{(0,0),(-1,1),(1,1),(-2,4),(2,4),(-3,9),(3,9)\}$
3. $\{(0,0),(1,1),(4,2),(9,3),(16,4),(25,5),(36,6)\}$

17.10 (Locus from Lines) Determine an equation, or equations, to represent the locus of points equidistant from each pair of lines.

1. $y=x$ and $y=-x$
2. $y=2x+2$ and $y=-2x+2$
3. $y=2x$ and $y=0.5x$

17.11 (Locus from Radicals) Determine an equation, or equations, to represent the locus of points equidistant from each pair of graphs.

1. $y=-{\sqrt {x}}$ and $y={\sqrt {x}}$
2. $y={\sqrt {x}}+4$ and $y=-{\sqrt {x}}-6$

17.12 (Flower Bed) The outside edge of a fountain is the locus of points 2 meters from the center. The outside edge of a flower bed is the locus of points 3 meters from the center of the fountain. There is no gap between the fountain and the flower bed. Sketch the flower bed, and find its area.

17.13 (Describing Loci) Describe and list the locus of points in the plane that are 13 units from the origin, and 12 units from the y-axis.

17.14 (Three Times the Distance) Find the equation of locus of a point such that its distance from the origin is three times its distance from the x-axis.

Section 17.3

17.15 (Identifying Conic Sections) Identify the conic section represented by the equations below.

Section 17.4

17.16 (Circle) If a circle passes through the points (0,0), (a,0), and (0,b), what are the coordinates of its center?

Section 17.8

17.17 (Rotation of Axes) Find the XY-coordinates of each of the given points if the axes are rotated through the specified angle.

Reason and Apply

17.18 (Have a Point!) Name a point that is ${\sqrt {2}}$ units away from (-1, 5).