Name:_______________________________________ Geometry Date:__________________ Unit 5 Study Guide

TOPICS: formulas(slope, distance, midpoint, line, circle), equations of lines (median, altitude, and perpendicular bisector, side of a special type of quadrilateral), area & perimeter using coordinate geometry, directed line segment, determining center and radius of equation of a circle, coordinate geometry proofs, analytic geometry Please do all problems on loose leaf paper. Show all expected work.

1. M(-2, 10) is the midpoint of AB . If A has coordinates (4, -5), what are the coordinates of B?

Equations of Lines

2. E, D and V are points with coordinates (0, -5), (2, -11) and (8, 1). Find the equation of EH the altitude of triangle EDV.

3. A, B, and C are points with coordinates A (1,2), B (6,3) and C(4, 11). Find the equation of altitude .BV 4. Triangle PQR has vertices P(3,0), Q(7,0) and R(5, -3). a. Find the equation of line RM, the median through R. b. Find the equation of line PN, the median through P. 5. In triangle ABC, A(0,5), B (6,9) and C(0,12). a. Find the equation of the perpendicular bisector line of AC. b. Find the equation of the perpendicular bisector line of AB. 6. Given parallelogram ABCD.

If A(1, 4) and B(4, 10), find the equation of the line containing CD if Q(6, -2) lies on CD .

7. Given rectangle FROG with F(-3, 1) and O(-1, 11), find GM, where M is the midpoint of GM .

8. Given rectangle JUMP with J(5, -7) and U(2, -9), find the equation of the line containing UM .

9. RSTU is a rhombus with R(-4,-2) and T(6, -4). Find the equation of the diagonal .SU

AREA & PERIMETER on Cartesian graph

10. 11.

Partitioning of directed line segment

12. Find the coordinates of point P, that lies 3

2of the way on the directed line segment AB ,

given A (-2, 5) and B (4, 9).

13. Find the coordinates of point P that lies on the line segment MQ , M(-9, -5), Q(3, 5), and partitions the

segment at a ratio of 2 to 5. 14. Cleve’s Cookie Store is located at the corner of 2nd Avenue and 9th Street. Dave’s Doorknobs is located at the corner of 12th Avenue and 14th Street. Located 1/5 of the distance from Cleve’s Cookie Store is the post office. Where is the post office?

Equations of Circles

15. State the center and radius of each circle.

a.) 2 23 100x y b.)

2 25 1 24x y

16. Write the equation of the circle, in center-radius form, which satisfies the given criteria. Center (-6, -1) and a radius of 3.

17. Find the equation of the circle which has a diameter with endpoints of (-6, 4) and (12,8). 18. Write the equation of the circle with center (-2, 5) and passes through (4, -3). 19. Determine the center and radius of the given circles by completing the square.

a. 2 2 4 14 17 0x y x y b. 2 2 4 16 52 0x y x y

c. 2 214 2 50 0x x y y d. 2 2 18 17 0x y x

Coordinate Geometry Proofs

20. Show Triangle XYZ is an isosceles right triangle. X(4, -1), Y(5,6) and Z(1,3) 21. The vertices of quadrilateral PQRS are P(0,2), Q(4,8), R(7,6), and S(3,0). Prove that PQRS is a rectangle.

22. Quadrilateral ABCD has vertices A(-3,6), B(6,0), C(9,-9), and D(0,-3). Prove that ABCD is a parallelogram but NOT a rhombus. 23. Quadrilateral DEFG has vertices D(-4,0), E(0,1), F(4,-1), and G(-4,-3). Show that DEFG is a trapezoid but NOT an isosceles trapezoid.

24. Quadrilateral MATH has coordinates , , , and . Prove that quadrilateral

MATH is a rhombus and prove that it is not a square.

Analytic Geometry 25. Determine the missing vertex or coordinates of the shape.

26. In the coordinate plane, the vertices of are

, , and .

(a) Prove that is a right triangle.

(b) State the coordinates of point P such that quadrilateral

RSTP is a rectangle.

(c) Prove that your quadrilateral RSTP is a rectangle.

[The use of the set of axes is optional.]