*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

**19. Parallelogram ABCD has coordinates A(0,7) and C(2,1). Which statement would prove that ABCD is a rhombus?**

(3) ** The slope of BD is 1/3.**.

The diagonals of a rhombus are perpendicular. That means that the slopes of the diagonals are *inverse reciprocals*.

The slope of AC is (1 - 7) / (2 - 0) = -6 / 2 = -3.

Therefore, the slope of BD must be +1/3.

The midpoint of AC is (1, 4), which would be true regardless of the shape of the parallelogram. The length of diagonal BD is not restricted by the location of points A and C; the length of one diagonal does not affect the other. Finally, the slope of AC is NOT 1/3.

**20. Point Q is on such that MQ:QN = 2:3. If M has coordinates (3,5) and N has coordinates (8,-5), the coordinates of Q are
**

(1) *(5, 1)*

2 + 3 = 5, so Q is 2/5 of the way from M to N.

(2/5)(8 - 3) = +2 and (2/5)(-5 -5) = -4.

The coordinates of Q are (3 + 2, 5 - 4), or *Q(5, 1)*.

Continue to the next problems.

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