Geometry Problems of the Day (Geometry Regents, January 2014)

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, January 2014

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


32. A right prism has a square base with an area of 12 square meters. The volume of the prism is 84 cubic meters. Determine and state the height of the prism, in meters.

Answer:

The Volume of a prism is the Area of the Base times the height. You are given the Volume and the Area of the Base. Plug these in and solve.

84 = 12 h
7 = h

33. State whether the lines represented by the equations y = 1/2x - 1 and y + 4 = -1/2(x - 2) are parallel, perpendicular, or neither. Explain your answer.

Answer:

The lines are not parallel because they do not have the same slope. One line has a slope of 1/2 while the other has a slope of -1/2.

The liner are not perpendicular either. The products of their slopes is (1/2)(-1/2) = -1/4, not -1. The slopes are NOT inverse reciprocals.

The two lines are neither parallel nor perpendicular.

You need to include the word "neither" (not worth any points, but you will lose points if you don't state it) AND a reason why they are not parallel and why they are not perpendicular (each reason worth 1 credit).

If you just state "neither", you will earn zero credit.

34. A tree, T, is 6 meters from a row of corn, c, as represented in the diagram below. A farmer wants to place a scarecrow 2 meters from the row of corn and also 5 meters from the tree.

Sketch both loci.

Indicate, with an X, all possible locations for the scarecrow.

Answer:

Five meters away from the tree means a circle with radius of 5. Since the row of corn is 6 meters away, the circle will come close to the line but not touch it. This is a sketch, so it doesn't have to be perfect.

Two meters away from the line of corn means two parallel lines on either side of the line. Since the circle comes within one meter of the line of corn, one of the parallel lines will intersect the circle in two places. Put an X on both of those places.

More to come. Comments and questions welcome.

More Regents problems.

I also write Fiction! You can now preorder Devilish And Divine, edited by John L. French and Danielle Ackley-McPhail, which contains (among many, many others) three stories by me, Christopher J. Burke about those above us and from down below. Preorder the softcover or ebook at Amazon.