Geometry Problems of the Day (Geometry Regents, August 2012)

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.

A(1,2) --> A'(-2,1)
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 r² h
= π (5)² (7)
= 175 π

More to come. Comments and questions welcome.

More Regents problems.

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