+1 862 207 3288 Fill in the following blanks and submit using the assignment tool in Module 2. You can fill in the blanks and submit as a word document. The second option is to print out the form, write the answers on the printout, scan your answers and submit your work as a PDF file.
Find the Midpoint of a Line Segment
To find the midpoint of a line segment, we simply ______________ the x- and y-coordinates , respectfully.
The midpoint of the line segment with endpoints (x_1,y_1 ) “and ” (x_2,y_2 ) is ((x_1+x_2)/2,(y_1+y_2)/2).
The midpoint M of the segment with endpoints (-3,-3) and (1,4) is ______________.
Finding the Distance between two points
The distance formula is based on the _____________________ Theorem.
The distance between A(x_1 〖,y〗_1 )” and ” B(x_2,y_2 )” is given by the formula:”
” ” d(A,B)=√((x_2-x_1 )^2+(y_2-y_1 )^2 )
Find the distance between P(-3,4) and R(2,-1)
Letting x1 = -3, x2 = 2, y1 = 4, and y2 = ______, we get: d(P,R)=√((2-[-3])^2+(-1-4)^2 )
Simplifying gives: √(5^2+〖(-5)〗^2 )=√50= _____√2.
III. Standard Form of the Equation of a Circle
A. A circle is the set of all points in a plane that are at a fixed distance from a fixed point. The fixed point is called the ____________ of the circle and the fixed distance is called the ______________ of the circle.
B. The standard form of an equation of a circle with center __________ and radius ______ is (x-h)^2+(y-k)^2=r^2
C. Find the standard form of the equation of a circle with center (2, -5) and radius 4.
1. In the standard form given in B, h = 2, k = -5 and r = 4 giving:
(x – _____ )2 + (____ + 5)2 = _______
D. Given the equation of a circle is (x – 4)2 + (y + 3)2 = 36:
1. The center of the circle is __________
2. The radius of the circle is _________.
3. To find the x-intercepts, set y = 0 and solve for x
a. (x – 4)2 + (0 + 3)2 = 36
b. x2 – 8x + 16 + _____ = 36
c. x2 – 8x – 11 = 0
d. x = (8±√(64-4(-11)))/2 = ________ or ___________ [round to nearest hundredth]
E. The _______________ form of the equation of a circle is: Ax2 + By2 +Cx +Dy + E = 0
F. Write the equation of the circle x2 + y2 – 2x + 6y + 1 = 0 in standard form and find the center and radius
1. Group the x-terms and y-terms on the left side of the equation:
x2 – 2x + y2 + 6y = -1
2. Complete the square with both the x-terms and the y-terms:
x2 – 2x + ____ + y2 + 6y + _____ = -1 + 1 + 9
3. Factoring the left side and simplifying the right side gives (x – 1)2 + (y + 3)2 = 9
4. The center of the circle is _________ and the radius is _________.
IV. Slope of a Line
A. A line going up from left to right has _____________ slope. A line going down from left to right has __________________ slope. Horizontal lines have _________ slope, and vertical lines have ________________ slope.
B. The slope can be computed by comparing the vertical change, or the _________, to the horizontal change, or the __________. The slope of a line through the points (x1, y1) and (x2, y2) is given by m=rise/run=(change in y)/(change in x)=(y_2-y_1)/(x_2-x_1 )
C. Find the slope of the line containing the points (3, -5) and (-2, 7). m = __________
V. Forms of the equation of a line
A. The point-slope form of the equation of a line is __________________________.
B. The slope-intercept form of the equation of a line is _______________________.
C. The standard form of the equation of a line is _________________________.
VI. Writing Equations of Lines
A. Write the equation of the line containing the point (-2, 1) and having slope 3:
1. y – 1 = ____ (x + _____)
2. Changing to slope-intercept form gives y = 3x + _____ .
B. Given the graph of a line, write the equation of the line in slope-intercept form:
y = _________________
C. Write the equation of the line containing (-1,2) and (3,5) in slope-intercept form.
1. The slope of the line (use the formula in IV. B above) is: ___________
2. Using the point (-1, 2) and the slope, write the equation in point-slope form:
y – ______ = (3/4)(x + ______)
3. Simplifying gives y = (3/4)x + ________.
D. The equation of a _______________________ line has the form y = b.
1. The equation of the horizontal line through the point (-4, 7) is ___________.
E. The equation of a _______________________ line had the form x = a.
1. The equation of the vertical line through the point (-3, 5) is ____________.
VII. To find the x-intercept of a line set ______ equal to zero and solve for _______. To find the y-intercept of a line set ______ equal to zero and solve for ______.
A. Find the x- and y-intercepts of the line given by 3x – 5y = 10.
1. To find the x-intercept, set y = 0: 3x – 5(0) = 10
2. Solve this equation for x; x = ______
3. To find the y-intercept, set x = 0: 3(0) – 5y = 10
4. Solve this equation for y: y = ______
VIII. _________________ lines are lines that never intersect, _____________________ lines intersect at a right angle.
A. Two distinct nonvertical lines in the Cartesian plane are parallel if and only if they have the __________ slope.
B. Two nonvertical lines in the Cartesian plane are perpendicular if and only if the product of their slopes is ________.
C. If the slope of line l1 is a/b:
1. l2 is parallel to l1 if the slope of l2 is ________.
2. l2 is perpendicular to l1 if the slope of l2 is ________.
D. Tell whether the lines y = 2x – 8 and x + 2y = 5 are parallel, perpendicular or neither.
1. the slope of y = 2x – 8 is _______.
2. the slope of x + 2y = 5 is _______.
3. therefore the lines are ____________________.
E. Find the equation of the line parallel to the line x = 8 and containing (4, 9).
1. x = 8 is a __________________ line. A line parallel to it will also be vertical.
2. Therefore the equation of the parallel line will have the form x = a.
3. Since it contains (4, 9), the equation will be x = ______.
F. Find the equation of the line perpendicular to the line 2x + 3y = 9 and passing through the point (2, 6).
1. Putting 2x + 3y = 9 into slope-intercept form gives: y = (-2/3)x + _____
2. The slope of this line is __________.
3. Therefore the slope of a line perpendicular to this is 3/2.
4. Write the equation of the perpendicular line in point-slope form: y – _____ = 3/2(x – ____).
5. Putting into slope-intercept form gives: y = (3/2)x + _____.
IX. Using a Graphing Calculator to Make Calculations
A. If you have not used a graphing calculator before, you should familiarize yourself with some basic skills at this time. Go the David Williamson’s Graphing Calculator Tutorials at http://dtc.pima.edu/~dwilliamson/TI/indexti.html . The index of tutorials will appear on the left side of the screen. Click on one of these topics to view it. The topics you should view at this time are:
1. Second Function Key
2. Basic Calculations & Editing
3. Basic Calculations – Negative #s
4. Basic Calculations – Exponents
5. Basic Calculations – Roots
B. Use the graphing calculator to evaluate: -5+3^2.1-∛2 to the nearest thousandth. ____________
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