Coordinate plane example

coordinate plane formula and coordinate plane math problems
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Published Date:26-07-2017
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MATH 1510 Lili Shen The Coordinate Fundamentals of Mathematics Plane Lines (MATH 1510) Instructor: Lili Shen Email: shenliliyorku.ca Department of Mathematics and Statistics York University October 7-9, 2015Outline MATH 1510 Lili Shen The Coordinate Plane Lines 1 The Coordinate Plane 2 LinesThe coordinate plane MATH 1510 The coordinate plane or Cartesian plane: Lili Shen y (y-axis) The Coordinate Plane Lines Quadrant II Quadrant I a: x-coordinate  P(a;b) b b: y-coordinate a x (x-axis) O (origin) Quadrant III Quadrant IVGraphing regions in the coordinate plane MATH 1510 Lili Shen The Coordinate Plane Lines Example Sketch the following sets in the coordinate plane: (1)f(x;y)j x 0g. (2)f(x;y)j y = 1g. (3)f(x;y)jjyj 1g.Graphing regions in the coordinate plane MATH 1510 Lili Shen Solution. (1) The Coordinate Plane y Lines x OGraphing regions in the coordinate plane MATH 1510 Lili Shen Solution. The (2) Coordinate Plane y Lines 1 x OGraphing regions in the coordinate plane MATH 1510 Solution. Lili Shen (3) The Coordinate y Plane Lines 1 x O 1The distance formula MATH 1510 Lili Shen The Coordinate Theorem Plane Lines The distance between points A(x ;y ) and B(x ;y ) in the 1 1 2 2 plane is È 2 2 d(A;B) = (x x ) +(y y ) : 2 1 2 1 This theorem can be easily proved by Pythagorean Theorem.Applying the distance formula MATH 1510 Lili Shen The Coordinate Plane Lines Example Which of the points P(1;2) or Q(8; 9) is closer to the point A(5; 3)?Applying the distance formula MATH 1510 Lili Shen The Coordinate Plane Solution. Lines Since È p 2 2 d(P;A) = (1 5) +(2 3) = 41; È p 2 2 d(Q;A) = (8 5) +(9 3) = 45; it follows that P is closer to A.The midpoint formula MATH 1510 Lili Shen The Coordinate Plane Lines Theorem The midpoint of the line segment from A(x ;y ) to B(x ;y ) 1 1 2 2 is   x +x y +y 1 2 1 2 ; : 2 2Applying the midpoint formula MATH 1510 Lili Shen The Coordinate Plane Lines Example Show that the quadrilateral with vertices P(1; 2), Q(4; 4), R(5; 9), and S(2; 7) is a parallelogram by proving that its two diagonals bisect each other.Applying the midpoint formula MATH 1510 Lili Shen Solution. The Coordinate The midpoint of the diagonal PR is Plane Lines     1+ 5 2+ 9 11 ; = 3; ; 2 2 2 and the midpoint of the diagonal QS is     4+ 2 4+ 7 11 ; = 3; : 2 2 2 So the two diagonals of the quadrilateral PQRS bisect the other, and thus it is a parallelogram.Graphs of equations in two variables MATH 1510 Lili Shen The Coordinate Plane Lines 2 An equation in two variables, such as y = x + 1, expresses a relationship between two quantities. The graph of an equation in x and y is the set of points (x;y) in the coordinate plane that satisfy the equation.Intercepts MATH 1510 Lili Shen The Coordinate Plane The x-coordinates (resp. y-coordinates) of the points where Lines a graph intersects the x-axis (resp. y-axis) are called the x-intercepts (resp. y-intercepts) of the graph. x-intercepts (resp. y-coordinates) can be found by setting y = 0 (resp. x = 0) and solve for x (resp. y).Finding intercepts MATH 1510 Lili Shen The Coordinate Plane Lines Example Find the x-intercepts and y-intercepts of the graph of the 2 equation y = x 2.Finding intercepts MATH 1510 Lili Shen The Coordinate Plane Solution. Lines 2 Let y = 0 one has x 2 = 0. Solving for x one obtains the p p x-intercepts 2 and 2. Next, we set x = 0 and get y =2. Thus the y-intercept is 2.Circles MATH 1510 Lili Shen The Coordinate Definition Plane Lines An equation of the circle with center (h;k) and radius r is 2 2 2 (xh) +(yk) = r : This is called the standard form for the equation of the circle. If the center of the circle is (0; 0), then the equation is 2 2 2 x +y = r :Finding an equation of a circle MATH 1510 Lili Shen The Coordinate Plane Lines Example Find an equation of the circle that has the points P(1; 8) and Q(5;6) as the endpoints of a diameter.Finding an equation of a circle MATH 1510 Lili Shen Solution. The The center of the circle is the midpoint of PQ: Coordinate Plane   1+ 5 8 6 Lines ; = (3; 1): 2 2 Let the radius of the circle be r. Then 2 2 2 r = (1 3) +(8 1) = 53: Therefore the equation of the circle is 2 2 (x 3) +(y 1) = 53:

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