Graphs

Find an equation of the line with slope 5 and x-intercept 2.

True or False Perpendicular lines have slopes that are reciprocals of one another.

In Problems 5–16, use a graphing utility to approximate the real solutions, if any, of each equation rounded to two decimal places. All solutions lie between - 10 and 10.$x^4- 5x^2 + 2x + 11 = 0$

Write each complex number in the standard form a + bi and plot each in the complex plane.

$2(\cos {150}^o+i\sin {150}^o)$

Find the midpoint of the line segment joining the points P₁ and P₂ .

$P_1=(-5,-3); P_2=(11,9)$

On a real number line the origin is assigned the number _________ .

If $-3$ and 5 are the coordinates of two points on the real number line, the distance between these points is _________.

If 3 and 4 are the legs of a right triangle, the hypotenuse is _________.

Use the converse of the Pythagorean Theorem to show that a triangle whose sides are of lengths 11, 60, and 61 is a right triangle.

The area of a triangle whose base is $b$ and whose altitude is $h$ is $A=$ _________.

True or False Two triangles are congruent if two angles and the included side of one equals two angles and the included side of the other.

If $(x,y)$ are the coordinates of a point P in the xy-plane, then x is called the ________ of P and y is the ________ of P.

The coordinate axes divide the xy-plane into four sections called _________.

If three distinct points P, Q, and R all lie on a line and if $d(P,Q)=d(Q,R)$, then Q is called the _________ of the line segment from P to R.

True or False The distance between two points is sometimes a negative number.

True or False The point $(-1,4)$ lies in quadrant IV of the Cartesian plane.

True or False The midpoint of a line segment is found by averaging the x-coordinates and averaging the y-coordinates of the endpoints.

In Problems 13 and 14, plot each point in the xy-plane. Tell in which quadrant or on what coordinate axis each point lies.

$$\begin{gathered} \left(a\right) A(-3,2) \\ \left(b\right) B(6,0) \\ \left(c\right) C(-2,-2) \\ \left(d\right) D(6,5) \\ \left(e\right) E(0,-3) \\ \left(f\right) F(6,-3) \end{gathered}$$

In Problems 13 and 14, plot each point in the xy-plane. Tell in which quadrant or on what coordinate axis each point lies.

$$\begin{gathered} \left(a\right) A=(1,4) \\ \left(b\right) B=(-3,-4) \\ \left(c\right) C=(-3,4) \\ \left(d\right) D=(4,1) \\ \left(e\right) E=(0,1) \\ \left(f\right) F=(-3,0) \end{gathered}$$

Plot the points $(2,0), (2,-3), (2,4), (2,1),$ and $(2,-1)$. Describe the set of all points of the form $(2,y)$, where y is a real number.

Plot the points $(0,3), (1,3), (-2,3), (5,3),$ and $(-4,3)$. Describe the set of all points of the form $(x,3)$, where x is a real number.

Determine the coordinates of the points shown. Tell in which quadrant each point lies. Assume the coordinates are integers.

Determine the coordinates of the points shown. Tell in which quadrant each point lies. Assume the coordinates are integers.

Determine the coordinates of the points shown. Tell in which quadrant each point lies. Assume the coordinates are integers.

Determine the coordinates of the points shown. Tell in which quadrant each point lies. Assume the coordinates are integers.

Select a setting so that each given point will lie within the viewing window.

$\left(-10,5\right),(3,-2),(4,-1)$

Select a setting so that each given point will lie within the viewing window.
$\left(5,0\right),(6,8),(-2,-3)$

Select a setting so that each given point will lie within the viewing window.

$\left(40,20\right),(-20,-80),(10,40)$

Select a setting so that each given point will lie within the viewing window.

$\left(-80,-60\right),(20,-30),(-20,-40)$

Select a setting so that each given point will lie within the viewing window.
$\left(0,0\right),(100,5),(5,150)$

Select a setting so that each given point will lie within the viewing window.

$\left(0,-1\right),(100,50),(-10,30)$

Determine the viewing window used.

Determine the viewing window used.

Determine the viewing window used.

Determine the viewing window used.

Determine the viewing window used.

Determine the viewing window used.

Find the distance $d(P_1,P_2)$between the points $P_1$and $P_2.$

Find the distance $d(P_1,P_2)$between the points  $P_1$and $P_2.$

Find the distance $d(P_1,P_2)$between the points $P_1$and $P_2.$

Find the distance $d(P_1,P_2)$between the points  $P_1$and $P_2.$

Find the distance $d(P_1,P_2)$between the points $P_1$and $P_2.$

$P_1(3,-4) \text{and} P_2(5,4).$

Find the distance $d(P_1,P_2)$ between the points $P_1$and $P_2.$

Find the distance $d(P_1,P_2)$between the points $P_1$ and $P_2.$

Find the distance $d(P_1,P_2)$between the points $P_1$and $P_2.$

Find the distance $d (P_1, P_2)$ between the points $P_1 \mathrm{and} P_2$.

$P_1=(4,-3); P_2=(6,4)$

Find the distance $d (P_1, P_2)$ between the points $P_1 \mathrm{and} P_2$.

$P_1=(-4,-3); P_2=(6,2)$

Find the distance $d (P_1, P_2)$ between the points $P_1 \mathrm{and} P_2$.

$P_1=(a,b); P_2=(0,0)$

Find the distance $d (P_1, P_2)$between the points $P_1 \mathrm{and} P_2$.

$P_1=(a,a); P_2=(0,0)$

Find the length of the line segment. Assume that the endpoints of each line segment have integer coordinates.