Section 1
Rectangular Coordinate Systems
Plot the points $A(5,-2), B(-5,-2), C(5,2), D(-5,2)$$E(3,0),$ and $F(0,3)$ on a coordinate plane.
Plot the points $A(-3,1), B(3,1), C(-2,-3), D(0,3),$ and $E(2,-3)$ on a coordinate plane. Draw the line segments$A B, B C, C D, D E,$ and $E A$
Plot the points $A(0,0), B(1,1), C(3,3), D(-1,-1),$ and $E(-2,-2) .$ Describe the set of all points of the form(a, a), where $a$ is a real number.
Plot the points $A(0,0), B(1,-1), C(3,-3), D(-1,1)$ and $E(-3,3) .$ Describe the set of all points of the form$(a,-a),$ where $a$ is a real number.
Find the coordinates of the points $A-F$.(GRAPH CANT COPY)
Describe the set of all points $P(x, y)$ in a coordinate plane that satisfy the given condition.(a) $x=-2$(b) $y=5$(c) $x \geq 0$(d) $x y>0$(e) $y<0$(f) $x=0$
Describe the set of all points $P(x, y)$ in a coordinate plane that satisfy the given condition.(a) $y=-2$(b) $x=4$(c) $x / y<0$(d) $x y=0$(e) $y>1$(f) $y=0$
(a) Find the distance $d(A, B)$ between $A$ and $B$ (b) Find the midpoint of the segment $A B$$$A(4,-3), \quad B(6,2)$$
(a) Find the distance $d(A, B)$ between $A$ and $B$ (b) Find the midpoint of the segment $A B$$$A(-2,-5), \quad B(4,6)$$
(a) Find the distance $d(A, B)$ between $A$ and $B$ (b) Find the midpoint of the segment $A B$$$A(-7,0), \quad B(-2,-4)$$
(a) Find the distance $d(A, B)$ between $A$ and $B$ (b) Find the midpoint of the segment $A B$$$A(5,2), \quad B(5,-2)$$
(a) Find the distance $d(A, B)$ between $A$ and $B$ (b) Find the midpoint of the segment $A B$$$A(7,-3), \quad B(3,-3)$$
(a) Find the distance $d(A, B)$ between $A$ and $B$ (b) Find the midpoint of the segment $A B$$$A(-4,7), \quad B(0,-8)$$
Show that the triangle with vertices $A, B$ and $C$ is a right triangle, and find its area.(GRAPH CANT COPY)
Show that $A(-4,2), B(1,4), Q(3,-1),$ and $D(-2,-3)$ are vertices of a square.
Show that $A(-4,-1), B(0,-2), Q(6,1),$ and $D(2,2)$ are vertices of a parallelogram.
Given $A(-3,8),$ find the coordinates of the point $B$ such that $Q(5,-10)$ is the midpoint of segment $A B$
Given $A(5,-8)$ and $B(-6,2) .$ find the point on segment $A B$ that is three-fourths of the way from $A$ to $B$.
Prove that $C$ is on the perpendicular bisector of segment $A B.$$$A(-4,-3), \quad B(6,1), \quad Q,-6)$$
Prove that $C$ is on the perpendicular bisector of segment $A B.$$$A(-3,2), \quad B(5,-4), \quad O(7,7)$$
Find a formula that expresses the fact that an arbitrary point $P(x, y)$ is on the perpendicular bisector $I$ of segment $A B.$$$A(-4,-3), B(6,1)$$
Find a formula that expresses the fact that an arbitrary point $P(x, y)$ is on the perpendicular bisector $I$ of segment $A B.$$$A(-3,2), B(5,-4)$$
Find a formula that expresses the fact that $P(x, y)$ is a distance 5 from the origin. Describe the set of all such points.
Find a formula that states that $P(x, y)$ is a distance $r>0$ from a fixed point $C(h, k) .$ Describe the set of all such points.
Find all points on the $y$ -axis that are a distance 6 from $P(5,3)$
Find all points on the $x$ -axis that are a distance 5 from $P(-2,4)$
Find the point with coordinates of the form ( $2 a, a$ ) that is in the third quadrant and is a distance 5 from $P(1,3)$
Find all points with coordinates of the form $(a, a)$ that are a distance 3 from $P(-2,1)$
For what values of $a$ is the distance between $P(a, 3)$ and $Q(5,2 a)$ greater than $\sqrt{26} ?$
Given $A(-2,0)$ and $B(2,0),$ find a formula not containing radicals that expresses the fact that the sum of the distances from $P(x, y)$ to $A$ and to $B,$ respectively, is 5
Prove that the midpoint of the hypotenuse of any right triangle is equidistant from the vertices.
Prove that the diagonals of any parallelogram bisect each other.
Plot the points in the given viewing rectangle.$$\begin{aligned}&A(-5,-3.5), B(-2,2), Q(1,0.5), D(4,1), \text { and } E(7,2.5)\\&\text { in }[-10,10] \text { by }[-10,10]\end{aligned}$$
Plot the points in the given viewing rectangle.$$\begin{aligned}&A(-10,4), \quad B(-7,-1.1), \quad(0,-6), \quad D(3,-5.1), \text { and }\\&E(9,2.1) \text { in }[-12,12] \text { by }[-8,8]\end{aligned}$$
Plot the points in the given viewing rectangle.The table lists the number of U.S. households with a computer for selected years.$$\begin{array}{|c|c|}\hline \text { Year } & \text { Households (in thousands) } \\\hline 1984 & 87,073 \\\hline 1993 & 98,736 \\\hline 2003 & 113,126 \\\hline 2009 & 119,296 \\\hline\end{array}$$(a) Plot the data in the viewing rectangle $[1982,2012]$ by $\left[80 \times 10^{3}, 120 \times 10^{3}, 10 \times 10^{3}\right]$(b) Discuss how the number of households is changing.
Plot the points in the given viewing rectangle.The table lists the number of daily newspapers published in the United States for various years.(a) Plot the data in the viewing rectangle $[1895,2005,10]$ by $[0,3000,1000]$(b) Use the midpoint formula to estimate the number of newspapers in $1930 .$ Compare your answer with the true value, which is 1942 .$$\begin{array}{|c|c|}\hline \text { Year } & \text { Newspapers } \\\hline 1900 & 2226 \\\hline 1920 & 2042 \\\hline 1940 & 1878 \\\hline 1960 & 1763 \\\hline 1980 & 1745 \\\hline 2000 & 1480 \\\hline\end{array}$$