Geometry Regents Exam - June 2024

Geometry Regents New York State Exam - June 2024

Geometry Regents New York State Exam Questions June 2024 (pdf)

Geometry Regents Exam June 2024 (Solutions 1 - 35)

1. In the diagram below, △BRI is the image of △JOE after a translation. Triangle CAT is the image of △BRI after a line reflection.
2. A right cylinder is cut parallel to its base. The shape of this cross section is a
3. What is the minimum number of degrees that a regular hexagon must rotate about its center to carry it onto itself?
4. In the diagram below, a sphere is inscribed inside a cube. The cube has edge lengths of 18.
5. In the diagram below
6. Which equation represents the line that passes through the point (2,-7) and is perpendicular to the line whose equation is y = 3/4 x + 4?
7. In △RHM below
8. The funnel shown below can be used to decorate cookies with melted chocolate. The funnel can be modeled by a cone whose radius is 6 cm and height is 13 cm. The baker uses 2 cubic centimeters of chocolate to decorate each cookie. When the funnel is completely filled, what is the maximum number of cookies that can be decorated with the melted chocolate?
9. In circle O below
10. In the diagram below
11. In circle O below, OA = 6, and m/COA = 100°.
12. In rectangle ABCD, diagonal AC is drawn. The measure of ∠ACD is 37° and the length of BC is 7.6 cm. What is the length of AC, to the nearest tenth of a centimeter?
13. A peanut butter manufacturer would like to use a cylindrical jar with a volume of 1180 cm3. The jar has a height of 10 cm. What is the diameter of the jar, to the nearest tenth of a centimeter?
14. Triangle KLM is dilated by a scale factor of 3 to map onto triangle DRS. Which statement is not always true?
15. A rectangle with dimensions of 4 feet by 7 feet is continuously rotated about one of its 4-foot sides. The resulting three-dimensional object is a 12 inches. Which two-dimensional figure shows a cross section that is perpendicular to the base and passes through the center of the base?
16. In right triangle ABC, altitude CD is drawn to hypotenuse AB. If AD = 4 and CD = 8, the length of BD is
17. If ABCD is a parallelogram, which additional information is sufficient to prove that ABCD is a rectangle?
18. Line segment APB has endpoints A(-5,4) and B(7,-4). What are the coordinates of P if AP:PB is in the ratio 1:3?
19. In the diagram below, AB and CD intersect at E, and CA and DB are drawn.
20. If sin(3x + 9)° = cos(5x - 7)°, what is the value of x?
21. Which set of integers could represent the lengths of the sides of an isosceles triangle?
22. In the diagram shown below, altitude CD is drawn to the hypotenuse of right triangle ABC.
23. Which congruence statement is sufficient to prove parallelogram MARK is a rhombus?
24. A line whose equation is y = -2x + 3 is dilated by a scale factor of 4 centered at (0,3). Which equation represents the image of the line after the dilation?
25. In △ABC below, m∠C = 90°, AC = 11, and AB = 18. Determine and state the measure of angle A, to the nearest degree.
26. Use a compass and straightedge to construct an equilateral triangle inscribed in circle A below.
27. Quadrilateral DEAR and its image, quadrilateral D’E’A’R’, are graphed on the set of axes below
28. In circle P below, tangent AL and secant AKE are drawn.
29. The equation of a circle is x² + y² + 8x - 6y + 7 = 0. Determine and state the coordinates of the center and the length of the radius of the circle.
30. On the set of axes below, △ABC is drawn with vertices that have coordinates A(2,-3), B(4,5), and C(-5,1).
31. In the diagram below, AE = 15, EB = 27, AF = 20, and FC = 36.
32. A building is composed of a rectangular pyramid on top of a rectangular prism, as shown in the diagram below. The rectangular prism has a length of 38 feet, a width of 15 feet, and a height of 22 feet. The rectangular pyramid sits directly on top of the rectangular prism, and its height is 12 feet. An air purification filter was installed that will clean all the air in the building at a rate of 2400 cubic feet per minute. Determine and state how long it will take, to the nearest tenth of a minute, for the filter to clean the air contained in the building.
33. Given:
34. In the diagram below, a boat at point A is traveling toward the most powerful waterfall in North America, the Horseshoe Falls. The Horseshoe Falls has a vertical drop of 188 feet. The angle of elevation from point A to the top of the waterfall is 15°. After the boat travels toward the falls, the angle of elevation at point B to the top of the waterfall is 23°. Determine and state, to the nearest foot, the distance the boat traveled from point A to point B.
35. Triangle JOE has vertices whose coordinates are J(4,6), O(-2,4), and E(6,0). Prove that △JOE is isosceles

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