Topic 9 Ms. Helgeson Coordinate Geometry

9.1 Polygons in the Coordinate Plane What formulas can you use to identify properties of figures on the coordinate plane? Distance Formula Midpoint Formula Slope Formula

The vertices of ∆PQR are P(4, 1), Q(2, 7), and Is ∆PQR equilateral, isosceles, or scalene? Explain. Is ∆PQR a right triangle? Explain.

The vertices of a parallelogram are A(-2, 2), B(4, 6), C(6, 3), and D(0, -1). Is ABCD a rhombus? Explain. Is ABCD a rectangle? Explain.

The vertices of a quadrilateral are Q(2, 5), R(7, 6), S(6, 1), and P(2, 1). Is QRST a kite, trapezoid, or neither?

The vertices of WXYZ are W(5, 4), X(2, 9), Y(9, 9), and Z(8, 4). What is the perimeter of WXYZ? What is the area of WXYZ?

9.2 Proofs Using Coordinate Geometry p 393 How can you use coordinates to prove geometric relationships algebraically? Plan a proof for the Trapezoid Midsegment Theorem. Theorem: The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases. P 393 - 394

Write a coordinate proof of the Concurrency of Medians Theorem Write a coordinate proof of the Concurrency of Medians Theorem. Given: ∆ABC with medians AD, BE, and CF. Prove: EF ║ AD ║ BC and EF = AD + BC 2 B(a, b) C(c, b) F E A(0, 0) O D(d, 0)

Write a coordinate ₂AD, BE, and CF Write a coordinate ₂AD, BE, and CF. Prove: The medians are concurrent at point P such that AP = 2/3 AD, BP = 2/3 BD and CP = 2/3 CF. Centroid Formula x ₁ + x₂ + x₃ , y₁ + y₂ + y₃ 3 3 B(2a, 2b) F D A(0, 0) C(2c, 0) E

9.3 Circles in the Coordinate Plane

10.6 Equations of Circles Standard equation of a circle: x2 + y2 = r2 (x-h)2 + (y-k)2 = r2 If the center is the origin then the standard equation would be: x2 + y2 = r2

Examples 1.) Write the equation of the circle with the center (-4, 0) and radius 7 2.) Write the standard equation of a circle with center (-5, 0) and radius 4

Finding standard equations of the Circles. 1.) The point (1, 2) is on a circle whose center is (5, -1). 2.) The point (2, 1) is on the circle whose center is (4, -3). Hint: find the radius first!!!

Graph a Circle 1.) The equation of a circle is : (x + 2)2 + (y - 3)2 = 9 2.) Graph (x-3)2 + (y+1)2 = 4

9.4 Parabolas in the Coordinate Plane ?????????????