May Geometry Notes | Practice

Find the centroid given vertex (6, 0) and midpoint (0, 3)

(2, 2)

How far along is a 3 to 2 ratio point

three fifths of the way

Find the point dividing (2, 1) to (8, 7) in a ratio of 1 to 2

(4, 3)

Dilate the point (5, 4) with center (2, 1) and scale factor 2

(8, 7)

Rotate (4, 3) 90 degrees counterclockwise

(negative 3, 4)

Rotate (2, 5) 180 degrees

(negative 2, negative 5)

Rotate (2, 5) 270 degrees counterclockwise

(5, negative 2)

A figure has surface area 50 and volume 100. It is dilated by scale factor 3. Find the new surface area and volume

surface area equals 450, volume equals 2700

P of A equals 0.5, P of B equals 0.4, P of A and B equals 0.2. Are A and B independent?

yes, because 0.5 times 0.4 equals 0.2

P of A equals 0.6, P of B equals 0.3, P of A and B equals 0.12. Are A and B independent?

no, because 0.6 times 0.3 equals 0.18, which does not equal 0.12

The hypotenuse of a 30-60-90 triangle is 16. Find both legs

short leg equals 8, long leg equals 8 times the square root of 3

The long leg of a 30-60-90 triangle is 9 times the square root of 3. Find the hypotenuse

18

The hypotenuse of a 45-45-90 triangle is 10. Find the leg length

5 times the square root of 2

A square has a diagonal of 8. Find the side length

4 times the square root of 2

Two sides of a triangle are 7 and 10 and the included angle is 30 degrees. Find the area

17.5

Two sides of a triangle are 6 and 8 and the included angle is 45 degrees. Find the area

12 times the square root of 2

Angle A equals 40 degrees, angle B equals 60 degrees, side a equals 10. Find side b using Law of Sines

b is approximately 13.47

A triangle has sides b equals 5, c equals 7, and included angle A equals 60 degrees. Find side a using Law of Cosines

a equals the square root of 39, which is approximately 6.24

A triangle has sides a equals 8, b equals 6, c equals 5. Find angle A

A is approximately 92.9 degrees

Find the inverse of f of x equals 3x minus 5

f inverse of x equals the quantity x plus 5 divided by 3

Find the inverse of f of x equals the quantity x plus 2 divided by 4

f inverse of x equals 4x minus 2

An inscribed angle intercepts an arc of 140 degrees. Find the angle measure

70 degrees

A central angle intercepts an arc of 94 degrees. Find the angle measure

94 degrees

A circumscribed angle shares an arc with a central angle of 110 degrees. Find the circumscribed angle

70 degrees

A cyclic quadrilateral has three angles of 85, 95, and 72 degrees. Find the fourth angle

108 degrees

Convert 120 degrees to radians

2 pi over 3

Convert 3 pi over 4 to degrees

135 degrees

A sector has radius 6 and central angle pi over 3. Find the area

6 pi

A circle has radius 9 and central angle 2 pi over 3. Find the arc length

6 pi

A sector has radius 5 and central angle 80 degrees. Find the area

50 pi over 9, which is approximately 17.45

A square pyramid has base side 4 and height 6. Find the volume

32

A cone has radius 3 and height 9. Find the volume

27 pi

A trapezoid has bases 8 and 12 and height 5. Find the area

50

An equilateral triangle has side length 6. Find the area

9 times the square root of 3

A cone has radius 4 and slant height 9. Find the surface area

52 pi

A square pyramid has base side 6 and slant height 8. Find the surface area

132

A square has area 3 square feet. Convert to square inches

432 square inches

The altitude to the hypotenuse divides it into segments of 4 and 9. Find the altitude

6

The full hypotenuse is 13 and the segment adjacent to one leg is 4. Find that leg

2 times the square root of 13