Now that I'm caught up with the current New York State Regents exams, I'm revisiting some older ones.

More Regents problems.

*Geometry Regents, August 2012*

Part II: Each correct answer will receive 2 credits. Partial credit is available.

*29. Write the negation of the statement “2 is a prime number,” and determine the truth value of the
negation
*

**Answer: **

"2 is not a prime number."

This statement is false.

Negation means, basically, adding a "not" or removing a "not" that is already there. Negating a statement means it will have the opposite truth value from the original statement.

Since 2 *is* a prime number, the negation is false.

*30. The coordinates of the vertices of triangle ABC are A(1,2), B(-4,3), and C(-3,-5). State the
coordinates of triangle A'B'C', the image of triangle ABC after a rotation of 90° about the origin.
[The use of the set of axes below is optional.].
*

**Answer: **

If the direction of the rotation is not specified, then the rotation is

*counter-clockwise*. Think of the numbering of the quadrants. Quadrant I becomes Quadrant II, etc.

The rule for a rotation of 90 degrees counterclockwise is P(x, y) --> P'(-y, x). That is, switch the order of the x-coordinate and the y-coordinate and then switch the sign of the new x-coordinate.

B(-4,3) --> B'(-3,-4)

C(-3,-5) --> C'(5,-3)

*31.A cylinder has a height of 7 cm and a base with a diameter of 10 cm. Determine the volume, in
cubic centimeters, of the cylinder in terms of π.
*

**Answer: **

Remember to use the RADIUS and not the Diameter. Divide 10/2 to get Radius = 5.

V = π r^{2} h

= π (5)^{2} (7)

= 175 π

More to come. Comments and questions welcome.

More Regents problems.

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