6.1 Practice A Geometry Answers

Problem i

Reflect triangle \(ABC\) over the line \(x=\text-three\).

Translate the image by the directed line segment from \((0,0)\) to \((4,1)\).

What are the coordinates of the vertices in the terminal epitome?

triangle ABC graphed. A = -5 comma 2, B = -6 comma -1, C = -3 comma 0.

Solution

Problem 2

Three line segments grade the letter N. Rotate the letter Due north counterclockwise around the midpoint of segment \(BC\) past 180 degrees. Describe the result.

The letter N, formed by 3 line segments. 4 points on the endpoints of the segments. Starting at the bottom left, A. Moving upward, B. Slanting down and to the right, C. Moving upward, D.

Solution

Problem 3

Triangle \(ABC\) has coordinates \(A = (i, three), B = (2,0),\) and \(C = (4,i).\) The paradigm of this triangle after a sequence of transformations is triangle \(A'B'C'\) where \(A' = (\text-5,\text-3), B' = (\text-4,0),\) and \(C' = (\text-ii,\text-i).\)

Write a sequence of transformations that takes triangle \(ABC\) to triangle \(A'B'C'\).

Solution

Problem 4

Bear witness triangle \(ABC\) is congruent to triangle \(DEF\).

Triangles ABC and DEF. A at origin, B at 2 comma 0, C at 3 comma 4, D at 3 comma -1, E at 3 comma 1, F at -1 comma 2.

Solution

Problem 5

The density of water is 1 gram per cm³. An object floats in water if its density is less than h2o's density, and it sinks if its density is greater than water's. Will a 1.17 gram diamond in the shape of a pyramid whose base of operations has area 2 cm² and whose height is 0.5 centimeters sink or bladder? Explain your reasoning.

Solution

Trouble vi

Technology required. An oblique cylinder with a base of radius 2 units is shown. The top of the cylinder can be obtained by translating the base past the directed line segment \(AB\) which has length sixteen units. The segment \(AB\) forms a \(30^\circ\) angle with the plane of the base of operations. What is the volume of the cylinder?

Oblique cylinder. Endpoints of slant length labeled A, at bottom and B, at top.

Solution

Trouble seven

This blueprint began from the structure of an equilateral triangle. Record at least 3 rigid transformations (rotation, reflection, translation) you lot encounter in the design.