Geometry Midterm Review Regents

Which object is formed when right triangle RST shown below is rotated around leg RD?

• A pyramid with a square base

• an isosoceles Triangle

• a right triangle

• A cone

The vertices of triangle JKL havae coordinates J(5,1), K(-2, -3) and L(-4,1). Under which transformation is the image triangle J'K'L' not congruent to triangle JKL?

• a translation of two units to the right and two units down

• a counterclockwise rotation of 180 degrees around the origin

• a reflection over the x-axis

• a dilation with a scale factor of 2 and centered at the origin

The center of circle Q has coordinates (3, -2). If circle Q passes through R(7,1), what is the length of its diameter?

• 50

• 25

• 10

• 5

In the diagram below, congruent figures 1,2, and 3 are drawn. Which sequence of transformations maps figure 1 onto figure 2 and then figure 2 onto figure 3?

• a reflection followed by a translation

• a rotation followed by a translation

• a translation followed by a reflection

• a translation followed by a rotation

A parallelogram must be a rectangle when its

• diagonals are perpendicular

• diagonals are congruent

• opposite sides are parallel

• opposite sides are congruent

Given three distinct quadrilaterals, a square, a rectangle, and a rhombus, which quadrilaterals must have perpendicular diagonals?

• the rhombus only

• the rectangle and the square

• the rhombus and the square

• the rectangle, the rhombus and the square

Line segment RW has endpoints R(-4,5) and W(6,20). Point P is on RW such that RP:PW is 2:3. What are the coordinates of point P?

• (2,9)

• (0,11)

• (2,14)

• (10,2)

The diagram shows two intersecting paths within a circular garden. What is the length of the portion of the path marked x?

• 8 and 1/3

• 11

• 3

• 12

In the diagram below, tangent PA and secant PBC are drawn to circle O from external point P. If PB =4 and BC = 5, what is the length of PA?

• 20

• 9

• 8

• 6

For a circle of radius 7 feet, find the arc length s cut off by a central angle of 6 degrees

• 42 pi feet

• 7/10 pi feet

• 7/30 pi feet

• 7/15 pi feet