January 2024 Geometry Regents Exam (Pt 1 & 2)

Which expression is equal to sin 30°?

• tan 30°

• sin 60°

• cos 60°

• cos 30°

In the diagram of ΔSRA below, KP is drawn such that ∠SKP ≅ ∠SRA. If SK = 10, SP = 8, and PA = 6, what is the length of KR, to the nearest tenth?

• 4.8

• 7.5

• 8.0

• 13.3

A rectangle is graphed on the set of axes below. A reflection over which line would carry the rectangle onto itself?

• y = 2

• y = 10

• y = 1/2 x - 3

• y = -1/2 x + 7

The surface of the roof of a house is modeled by two congruent rectangles with dimensions 40 feet by 16 feet, as shown below. Roofing shingles are sold in bundles. Each bundle covers 33 1/3 square feet. What is the minimum number of bundles that must be purchased to completely cover both rectangular sides of the roof?

• 20

• 2

• 39

• 4

Which equation represents a line that is perpendicular to the line whose equation is y - 3x = 4?

• y = -1/3x - 4

• y = 1/3x + 4

• y = -3x + 4

• y = 3x - 4

A vertical mine shaft is modeled in the diagram below. At a point on the ground 50 feet from the top of the mine, a ventilation tunnel is dug at an angle of 47°.

• 47

• 54

• 68

• 73

On the set of axes below, △BLU has vertices with coordinates B(−3,−2), L(−2,5), and U(1,1). What is the area of △BLU?

• 11

• 12.5

• 14

• 17.1

In the diagram below, ΔCAR is mapped onto ΔBUS after a sequence of rigid motions. If AR = 3x + 4, RC = 5x - 10, CA = 2x + 6, and SB = 4x - 4, what is the length of SB?

• 6

• 16

• 20

• 28

In the diagram below, ΔGHJ is dilated by a scale factor of 1/2 centered at point B to map onto ΔCDF. If m∠DFC = 40°, what is m∠HJG?

• 20°

• 40°

• 60°

• 80°

Directed line segment AJ has endpoints whose coordinates are A(5,7) and J(-10,-8). Point E is on AJ such that AE:EJ is 2:3. What are the coordinates of point E?

• (1,-1)

• (-5,-3)

• (-4,-2)

• (-1,1)