*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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