Friday, April 14, 2017

Geometry Problems of the Day

The following problems were taken from the GEOMETRY (COMMON CORE) Regents Exam given on Thursday, January 26, 2017.
Previous problems can be found here.

Part 1

13. On the graph below, point A(3,4) and with coordinates B(4,3) and C(2,1) are graphed. What are the coordinates of B' and C' after undergoes a dilation centered at point A with a scale factor of 2?

(1) B'(5,2) and C'(1,-2) .
A dilation with scale factor 2 centered at A means that everything will be twice as far from A as it currently is.
Point B is 1 unit right and 1 unit down from A, so B' will be 2 units right and 2 units down from A, or (5, 2).
Point C is 1 unit left and 3 units down from A, so C' will be 2 units left and 6 units down from A, or (1, -2).

14. In the diagram of right triangle ADE below, BC || DE.

Which ratio is always equivalent to the sine of ∠A?

(3) BC / AB
Sine = Opposite / Hypotenuse. There are two right triangles containing Angle A. The sides opposite angle A are BC in the smaller triangle and DE in the bigger triangle. Note that because BC || DE, Angle ACB must be a right angle because it corresponds to Angle E. The hypotenuse of the smaller triangle is AB, and the hypotenuse of the bigger triangle is AD.
The two possible answers to this question, therefore, are BC / AB, and DE / AD. The answer is choice (3).

Continue to the next problems.

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