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More Lessons for the Regents High School Exam

More Lessons for Algebra

High School Math based on the topics required for the Regents Exam conducted by NYSED. The following are the worked solutions for the Geometry (Common Core) Regents High School Examination January 2019.

### Geometry Common Core Regents New York State Exam - January 2019

The following are questions from the past paper
Regents High School Geometry, January 2019 Exam (pdf). Scroll down the page for the step by step solutions.

Geometry - January 2019 Regents - Questions and solutions 1 - 12

1. After a dilation with center (0, 0), the image of DB is D'B'. If DB = 4.5 and D'B' = 18, the scale factor of this dilation is

2. In the diagram below, ABC with sides of 13, 15, and 16, is mapped onto DEF after a clockwise rotation of 90° about point P.

3. On the set of axes below, ABC has vertices at A(-2,0), B(2,-4), C(4,2), and DEF has vertices at D(4,0), E(-4,8), F(-8,-4).

4. The figure below shows a rhombus with noncongruent diagonals.

Which transformation would not carry this rhombus onto itself?

5. In the diagram below of circle O, points K, A, T, I, and E are on the circle, KAE and ITE are drawn, KE ≅ EI, and EKA ≅ EIT.

6. In right triangle ABC shown below, point D is on AB and point E is on CB such that AC || DE.

If AB = 15, BC = 12, and EC = 7, what is the length of BD?

7. In rhombus VENU, diagonals VN and EU intersect at S.

If VN = 12 and EU = 16, what is the perimeter of the rhombus?

8. Given right triangle ABC with a right angle at C, m∠B61°. Given right triangle RST with a right angle at T, m∠R = 29°.

9. A vendor is using an 8-ft by 8-ft tent for a craft fair. The legs of the tent are 9 ft tall and the top forms a square pyramid with a height of 3 ft

What is the volume, in cubic feet, of space the tent occupies?

10. In the diagram below of right triangle KMI, altitude IG is drawn to hypotenuse KM.

If KG 9 and IG 12, the length of is

11. Which three-dimensional figure will result when a rectangle 6 inches long and 5 inches wide is continuously rotated about the longer side?

12. Which statement about parallelograms is always true?

Geometry - January 2019 Regents - Questions and solutions 13 - 24

13. From a point on the ground one-half mile from the base of a historic monument, the angle of elevation to its top is 11.87°. To the nearest foot, what is the height of the monument?

14. The area of a sector of a circle with a radius measuring 15 cm is 75π cm^{2}. What is the measure of the central angle that forms the
sector?

15. Point M divides AB so that AM:MB = 1:2. If A has coordinates (-1,-3) and B has coordinates (8,9), the coordinates of M are

16. In the diagram below of triangle ABC, AC is extended through point C to point D, and BE is drawn to AC.

17. In the diagram below of right triangle ABC, AC = 8, and AB = 17.

Which equation would determine the value of angle A?

18. Francisco needs the three pieces of glass shown below to complete a stained glass window. The shapes, two triangles and a trapezoid, are measured in inches.

Glass can be purchased in rectangular sheets that are 12 inches wide. What is the minimum length of a sheet of glass, in inches, that Francisco must purchase in order to have enough to complete the window?

19. In the diagram of quadrilateral NAVY below, m∠YNA = 30°, m∠YAN = 38°, m∠AVY = 94°, and m∠VAY = 46°.

Which segment has the shortest length?

20. What is an equation of a circle whose center is (1,4) and diameter is 10?

21. On the set of axes below, ABC, altitude CG, and median CM are drawn.

Which expression represents the area of ABC?

22. In right triangle ABC, m∠C = 90° and AC ≠ BC. Which trigonometric ratio is equivalent to sin B?

23. As shown in the diagram below, the radius of a cone is 2.5 cm and its slant height is 6.5 cm

How many cubic centimeters are in the volume of the cone?

24. What is an equation of the image of the line y = 2/3 x - 4 after a dilation of a scale factor of 3/4 centered at the origin?

Geometry - January 2019 Regents - Questions and solutions Parts 2-4

25. Write an equation of the line that is parallel to the line whose equation is 3y + 7 = 2x and passes through the point (2,6).

26. Parallelogram ABCD is adjacent to rhombus DEFG, as shown below, and FC intersects AGD at H.

If m∠B = 118° and m∠AHC = 138°, determine and state m∠GFH

27. As shown in the diagram below, secants PWR and PTS are drawn to circle O from external point P

If m∠RPS = 35° and mRS = 121°, determine and state mWT.

28. On the set of axes below, ABC is graphed with coordinates A(-2,-1), B(3,-1), and C(-2,-4). Triangle QRS, the image of ABC, is graphed with coordinates Q(-5,2), R(-5,7), and S(-8,2).

Describe a sequence of transformations that would map ABC onto QRS.

29. Given points A, B, and C, use a compass and straightedge to construct point D so that ABCD is a parallelogram.

[Leave all construction marks.]

30. On the set of axes below, DEF has vertices at the coordinates D(1,-1), E(3,4), and F(4,2), and point G has coordinates (3,1). Owen claims the median from point E must pass through point G.

Is Owen correct? Explain why.

31. A walking path at a local park is modeled on the grid below, where the length of each grid square is 10 feet. The town needs to submit paperwork to pave the walking path. Determine and state, to the nearest square foot, the area of the walking path.

32. A triangle has vertices A(-2,4), B(6,2), and C(1,-1).

Prove that ABC is an isosceles right triangle.

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

33. Theresa has a rectangular pool 30 ft long, 15 ft wide, and 4 ft deep. Theresa fills her pool using city water at a rate of $3.95 per 100 gallons of water.

Nancy has a circular pool with a diameter of 24 ft and a depth of 4 ft. Nancy fills her pool with a water delivery service at a rate of $200 per 6000 gallons.

If Theresa and Nancy both fill their pools 6 inches from the top of the pool, determine and state who paid more to fill her pool. [1 ft^{3} water 7.48 gallons

34. As modeled in the diagram below, an access ramp starts on flat ground and ends at the beginning of the top step. Each step is 6 inches tall and 8 inches deep

If the angle of elevation of the ramp is 4.76°, determine and state the length of the ramp, to the nearest tenth of a foot.

Determine and state, to the nearest tenth of a foot, the horizontal distance, d, from the bottom of the stairs to the bottom of the ramp.

35. In the diagram of quadrilateral ABCD with diagonal AC shown below, segments GH and EF are drawn, AE ≅ CG, BE ≅ DG, AH ≅ CF, and AD ≅ CB. Prove: EF ≅ GH

More Lessons for the Regents High School Exam

More Lessons for Algebra

High School Math based on the topics required for the Regents Exam conducted by NYSED. The following are the worked solutions for the Geometry (Common Core) Regents High School Examination January 2019.

Geometry - January 2019 Regents - Questions and solutions 1 - 12

1. After a dilation with center (0, 0), the image of DB is D'B'. If DB = 4.5 and D'B' = 18, the scale factor of this dilation is

2. In the diagram below, ABC with sides of 13, 15, and 16, is mapped onto DEF after a clockwise rotation of 90° about point P.

3. On the set of axes below, ABC has vertices at A(-2,0), B(2,-4), C(4,2), and DEF has vertices at D(4,0), E(-4,8), F(-8,-4).

4. The figure below shows a rhombus with noncongruent diagonals.

Which transformation would not carry this rhombus onto itself?

5. In the diagram below of circle O, points K, A, T, I, and E are on the circle, KAE and ITE are drawn, KE ≅ EI, and EKA ≅ EIT.

6. In right triangle ABC shown below, point D is on AB and point E is on CB such that AC || DE.

If AB = 15, BC = 12, and EC = 7, what is the length of BD?

7. In rhombus VENU, diagonals VN and EU intersect at S.

If VN = 12 and EU = 16, what is the perimeter of the rhombus?

8. Given right triangle ABC with a right angle at C, m∠B61°. Given right triangle RST with a right angle at T, m∠R = 29°.

9. A vendor is using an 8-ft by 8-ft tent for a craft fair. The legs of the tent are 9 ft tall and the top forms a square pyramid with a height of 3 ft

What is the volume, in cubic feet, of space the tent occupies?

10. In the diagram below of right triangle KMI, altitude IG is drawn to hypotenuse KM.

If KG 9 and IG 12, the length of is

11. Which three-dimensional figure will result when a rectangle 6 inches long and 5 inches wide is continuously rotated about the longer side?

12. Which statement about parallelograms is always true?

13. From a point on the ground one-half mile from the base of a historic monument, the angle of elevation to its top is 11.87°. To the nearest foot, what is the height of the monument?

14. The area of a sector of a circle with a radius measuring 15 cm is 75π cm

15. Point M divides AB so that AM:MB = 1:2. If A has coordinates (-1,-3) and B has coordinates (8,9), the coordinates of M are

16. In the diagram below of triangle ABC, AC is extended through point C to point D, and BE is drawn to AC.

17. In the diagram below of right triangle ABC, AC = 8, and AB = 17.

Which equation would determine the value of angle A?

18. Francisco needs the three pieces of glass shown below to complete a stained glass window. The shapes, two triangles and a trapezoid, are measured in inches.

Glass can be purchased in rectangular sheets that are 12 inches wide. What is the minimum length of a sheet of glass, in inches, that Francisco must purchase in order to have enough to complete the window?

19. In the diagram of quadrilateral NAVY below, m∠YNA = 30°, m∠YAN = 38°, m∠AVY = 94°, and m∠VAY = 46°.

Which segment has the shortest length?

20. What is an equation of a circle whose center is (1,4) and diameter is 10?

21. On the set of axes below, ABC, altitude CG, and median CM are drawn.

Which expression represents the area of ABC?

22. In right triangle ABC, m∠C = 90° and AC ≠ BC. Which trigonometric ratio is equivalent to sin B?

23. As shown in the diagram below, the radius of a cone is 2.5 cm and its slant height is 6.5 cm

How many cubic centimeters are in the volume of the cone?

24. What is an equation of the image of the line y = 2/3 x - 4 after a dilation of a scale factor of 3/4 centered at the origin?

Geometry - January 2019 Regents - Questions and solutions Parts 2-4

25. Write an equation of the line that is parallel to the line whose equation is 3y + 7 = 2x and passes through the point (2,6).

26. Parallelogram ABCD is adjacent to rhombus DEFG, as shown below, and FC intersects AGD at H.

If m∠B = 118° and m∠AHC = 138°, determine and state m∠GFH

27. As shown in the diagram below, secants PWR and PTS are drawn to circle O from external point P

If m∠RPS = 35° and mRS = 121°, determine and state mWT.

28. On the set of axes below, ABC is graphed with coordinates A(-2,-1), B(3,-1), and C(-2,-4). Triangle QRS, the image of ABC, is graphed with coordinates Q(-5,2), R(-5,7), and S(-8,2).

Describe a sequence of transformations that would map ABC onto QRS.

29. Given points A, B, and C, use a compass and straightedge to construct point D so that ABCD is a parallelogram.

[Leave all construction marks.]

30. On the set of axes below, DEF has vertices at the coordinates D(1,-1), E(3,4), and F(4,2), and point G has coordinates (3,1). Owen claims the median from point E must pass through point G.

Is Owen correct? Explain why.

31. A walking path at a local park is modeled on the grid below, where the length of each grid square is 10 feet. The town needs to submit paperwork to pave the walking path. Determine and state, to the nearest square foot, the area of the walking path.

32. A triangle has vertices A(-2,4), B(6,2), and C(1,-1).

Prove that ABC is an isosceles right triangle.

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

33. Theresa has a rectangular pool 30 ft long, 15 ft wide, and 4 ft deep. Theresa fills her pool using city water at a rate of $3.95 per 100 gallons of water.

Nancy has a circular pool with a diameter of 24 ft and a depth of 4 ft. Nancy fills her pool with a water delivery service at a rate of $200 per 6000 gallons.

If Theresa and Nancy both fill their pools 6 inches from the top of the pool, determine and state who paid more to fill her pool. [1 ft

34. As modeled in the diagram below, an access ramp starts on flat ground and ends at the beginning of the top step. Each step is 6 inches tall and 8 inches deep

If the angle of elevation of the ramp is 4.76°, determine and state the length of the ramp, to the nearest tenth of a foot.

Determine and state, to the nearest tenth of a foot, the horizontal distance, d, from the bottom of the stairs to the bottom of the ramp.

35. In the diagram of quadrilateral ABCD with diagonal AC shown below, segments GH and EF are drawn, AE ≅ CG, BE ≅ DG, AH ≅ CF, and AD ≅ CB. Prove: EF ≅ GH

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