Student Name: Teacher: Date: Miami-Dade County Public Schools. Test: 9_12 Mathematics Geometry Exam 2

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1 Student Name: Teacher: Date: District: Miami-Dade County Public Schools Test: 9_12 Mathematics Geometry Exam 2 Description: GEO Topic 5: Quadrilaterals and Coordinate Geometry Form: If the quadrilateral DEFG is a kite, what is m<f? 2. A line segment PQ has endpoint P at and Q at As a result of dilation about the origin, the endpoint of P' has coordinates What are the coordinates of Q'?

2 3. What is the equation of a line perpendicular to that intersects the line at 4. Trapezoid ABCD is such that sides and are parallel and Let,, and be three vertices of the trapezoid. Which value of a proves ABCD is a right trapezoid? 5. The figure below shows the parallelogram ABCD with segments AC and BD as diagonals. Which of these correctly proves that the diagonals of a parallelogram bisect each other?

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4 6. Examine the following coordinate grid. Point C is the midpoint of There exists a point D that is located on and is one-third of the way from C to What are the coordinates of D?

5 7. Rina draws a plan of her school on a coordinate grid. She plots the school gate at point and the library at point She notices that the science lab is also located on and is two-thirds the distance from the library to the school gate. What are the coordinates of the science lab? 8. Point divides the line segment joining points and such that What are the coordinates of point B? 9. What is the area, in square units, of the rectangle shown on the coordinate grid?

6 30 square units 32 square units 50 square units 110 square units 10. The line segment is shown below. Which transformation of will produce a line segment that is parallel to rotation of 180 about point B rotation of 90 about point B

7 reflection over the x-axis translation down 2 units 11. Triangle QRS has coordinates R(-6,9) and S(4,19). What coordinates of of point Q will give the triangle a perimeter of 39.1? (-12,15) (-4,25) (1,3) (6,-3) 12. Four students made observations about transformations. Which statement is true? Andrew: The transformation applied to a line segment yields a shorter line segment. Boris: The transformation applied to a line segment yields another line segment parallel to the first. Carlie: The transformation applied to an angle yields an angle with a greater measure. Deborah: The transformation applied to a circle yields a congruent circle. 13. On a coordinate plane, Triangle XYZ is rotated 90 degrees counterclockwise about the origin to form Triangle Which conclusion is always true?

8 14. Quadrilateral ABCD is graphed on a coordinate plane. Three of its vertices are at Which of the following additional statements is sufficient to prove that quadrilateral ABCD is a square? The slope of The length of are congruent. has a slope of 3 and a length of 15. Use the proof below to answer the question. Given: ABCD is a parallelogram Prove: and are supplementary. Proof: It is given that ABCD is a parallelogram with angles named, in consecutive order, Opposite angles of a parallelogram are congruent. Thus, by the definition of congruence. and The sum of the interior angles of any quadrilateral is 360, so Using the substitution property, Therefore,

9 By the division property of equality, Therefore, and are supplementary. What statements should go in the blanks of the proof? 16. Triangle XYZ with Point X at was dilated with the center at the origin to result in Point at Triangle was translated 3 units vertically to result in triangle Let p represent the perimeter, in units, of Triangle XYZ. Which expression represents the perimeter, in units, of Triangle 17. Quadrilateral has vertices at points and on a coordinate grid. The distance is 5 units and x is positive. Which whole number measure is closest to the perimeter of the quadrilateral? 18 units 19 units 20 units 26 units

10 18. Triangle PQR has vertices and Which best describes triangle PQR? a right triangle with a right triangle with an isosceles triangle with an isosceles triangle with 19. Given the line, what is the equation of a line that is perpendicular to the given line at the given line's x-intercept? 20. A directed line segment starts at and ends at Point R partitions the segment in the ratio of 2 to 1. What are the coordinates of point R?

11 21. Consider the line given by the equation. Which of the following gives the equation of a line parallel to the given line but with a different y-intercept? 22. Use the given proof to answer the question below: What can be proven in step 6 of this proof? I. The diagonals of this parallelogram bisect each other. II. The opposite sides of this parallelogram are congruent. III. Two opposite angles of this parallelogram are congruent.

12 I only III only II and III only I, II, and III 23. If the point (4, 7) is dilated by a factor of 10 about the point (1, 2), what are the coordinates of the image? 24. Which statement proves that quadrilateral UWXY is a parallelogram? Diagonals and bisect each other. Diagonals and are perpendicular. Sides and are congruent. Sides and are parallel. 25. Which equation of a line is parallel to the graph of and passes through the point

13 26. Consider the polygon in the xy-coordinate plane with vertices at points What is the most specific name for this polygon? kite parallelogram rectangle square 27. In the coordinate plane, which of the following functions dilates by a factor of 3 about the point (9, 6)?