Explanation Given: The triangle A ′ B ′ C ′ is the image of triangle ABC under the translation ( x , y ) → ( x + 3 , y − 5 ) . The coordinates of triangle A ′ B ′ C ′ are A ′ ( 0 , 7.91 ) , B ′ ( 5 − , 4 − .93 ) , C ′ ( 4.83 , 0 ) . Calculation: The coordinates of A ′ is ( 0 , 7.91 ) . The coordinates of point A under the translation ( x , y ) → ( x + 3 , y − 5 ) can be found as follows: 0 = x + 3 and 7.91 = y − 5 x = 0 − 3 and 7.91 + 5 = y x = 3 − and y = 12.91 So, the coordinates of A is ( 3 − , 12.91 ) . The coordinates of B ′ is ( 5 − , 4 − .93 ) . The coordinates of point B under the translation ( x , y ) → ( x + 3 , y − 5 ) can be found as follows: − 5 = x + 3 and − 4 To determine b. To find: The translation under which Δ A ′ B ′ C ′ is the image of Δ A B C .

13th Edition

ISBN: 9780135184103

Author: BOSCHMANS

Publisher: VST

See similar textbooks

Concept explainers

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These…

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are…

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) ge…

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.

Videos

Question

Chapter 14.CR, Problem 10CR

To determine

a.

To find:

The coordinates A, B, and C of the triangle ABC under the translation (x,y)→(x+3,y−5).

To determine

b.

To find:

The translation under which ΔA′B′C′ is the image of ΔABC.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.CR, Problem 9CR

Chapter 14.CR, Problem 11CR

Students have asked these similar questions

7. Show that for R sufficiently large, the polynomial P(z) in Example 3, Sec. 5, satisfies the inequality |P(z)| R. Suggestion: Observe that there is a positive number R such that the modulus of each quotient in inequality (9), Sec. 5, is less than |an|/n when |z| > R.

9. Establish the identity 1- 1+z+z² + 2n+1 ... +z" = 1- z (z1) and then use it to derive Lagrange's trigonometric identity: 1 1+ cos cos 20 +... + cos no = + 2 sin[(2n+1)0/2] 2 sin(0/2) (0 < 0 < 2л). Suggestion: As for the first identity, write S = 1+z+z² +...+z" and consider the difference S - zS. To derive the second identity, write z = eie in the first one.

8. Prove that two nonzero complex numbers z₁ and Z2 have the same moduli if and only if there are complex numbers c₁ and c₂ such that Z₁ = c₁C2 and Z2 = c1c2. Suggestion: Note that (i≤ exp (101+0) exp (01-02) and [see Exercise 2(b)] 2 02 Ꮎ - = = exp(i01) exp(101+0) exp (i 01 - 02 ) = exp(102). i 2 2

Chapter 14 Solutions

EBK A PROBLEM SOLVING APPROACH TO MATHE

Ch. 14.1 - Prob. 1MC Ch. 14.1 - Prob. 3MC Ch. 14.1 - Prob. 5MC Ch. 14.1 - Prob. 6MC Ch. 14.1 - Prob. 7MC Ch. 14.1 - A drawing of a cube, shown in the following...Ch. 14.1 - Wall stenciling has been used to obtain an effect...Ch. 14.1 - Prob. 10MC Ch. 14.1 - The following figure is a partial tessellation of...Ch. 14.1 - Prob. 12MC

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

a. To find: The coordinates A , B , and C of the triangle ABC under the translation ( x , y ) → ( x + 3 , y − 5 ) .

Solution Summary: The coordinates of A, B, and C of the triangle ABC under the translation (x,y)

Concept explainers

Videos

a.

To find:

The coordinates A, B, and C of the triangle ABC under the translation (x,y)→(x+3,y−5).

b.

To find:

The translation under which ΔA′B′C′ is the image of ΔABC.

Want to see the full answer?

Chapter 14 Solutions

a. To find: The coordinates A , B , and C of the triangle ABC under the translation ( x , y ) → ( x + 3 , y − 5 ) .

Solution Summary: The coordinates of A, B, and C of the triangle ABC under the translation (x,y)

Concept explainers

Videos

a. To find: The coordinates A, B, and C of the triangle ABC under the translation (x,y)→(x+3,y−5).

b. To find: The translation under which ΔA′B′C′ is the image of ΔABC.

Want to see the full answer?

Chapter 14 Solutions

a.

To find:

The coordinates A, B, and C of the triangle ABC under the translation (x,y)→(x+3,y−5).

b.

To find:

The translation under which ΔA′B′C′ is the image of ΔABC.