Q11. A point is translated from B聽to... [FREE SOLUTION]

91影视

Chapter 4: Q11. (page 179)

A point is translated from $B$ to $C$ as shown at the right. If a point at $(- 4, 3)$ is translated in the same way, what will be its new coordinates?
A $(3, 4)$ B $(1, 1)$ C $(- 7, 8)$ D $(1, 6)$

Short Answer

Expert verified

New coordinate is $B (1, 1)$

Step by step solution

- Vertex matrix

Let $(x, y)$ be an ordered pair then its vertex matrix will be $[\begin{matrix} x \\ y \end{matrix}]$

- Find vertex matrix for points B and C

From image coordinates of point $B$ and $C$ are $(- 1, 3)$ and $(4, 1)$

In vertex form point $[\begin{matrix} - 1 \\ 3 \end{matrix}]$ is translated to point $[\begin{matrix} 4 \\ 1 \end{matrix}]$

- Find translated matrix

When translation occurs, sum of vertex matrix of pre-image and translated matrix gives vertex matrix of image as shown below

$\begin{matrix} [\begin{matrix} 鈭� 1 \\ 3 \end{matrix}] + [\begin{matrix} x \\ y \end{matrix}] = [\begin{matrix} 4 \\ 1 \end{matrix}] \\ [\begin{matrix} 鈭� 1 + x \\ 3 + y \end{matrix}] = [\begin{matrix} 4 \\ 1 \end{matrix}] \end{matrix}$

As elements of both matrices are equal find values of x and y

\begin{matrix} 鈭� 1 + x = 4 \\ x = 4 + 1 \\ x = 5 \end{matrix}

and

\begin{matrix} 3 + y = 1 \\ y = 1 鈭� 3 \\ y = 鈭� 2 \end{matrix}

Thus, translated matrix is

[\begin{matrix} 5 \\ - 2 \end{matrix}]

- Find coordinate of new point

As point $(- 4, 3)$ with vertex matrix $[\begin{matrix} - 4 \\ 3 \end{matrix}]$ is translated with same translation matrix, so sum of vertex matrix of given point with translated matrix gives vertex matrix of new point as shown below

\begin{matrix} [\begin{matrix} 鈭� 4 \\ 3 \end{matrix}] + [\begin{matrix} 5 \\ 鈭� 2 \end{matrix}] = [\begin{matrix} 鈭� 4 + 5 \\ 3 鈭� 2 \end{matrix}] \\ = [\begin{matrix} 1 \\ 1 \end{matrix}] \end{matrix}

Thus, coordinate of new point is $(1, 1)$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

A point is translated from $B$ to $C$ as shown at the right. If a point at $(- 4, 3)$ is translated in the same way, what will be its new coordinates?
A $(3, 4)$ B $(1, 1)$ C $(- 7, 8)$ D $(1, 6)$

Short Answer

Step by step solution

- Vertex matrix

- Find vertex matrix for points B and C

- Find translated matrix

- Find coordinate of new point

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Calculus

Theoretical and Mathematical Physics

Probability and Statistics

Decision Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

91影视

A point is translated from Bto Cas shown at the right. If a point at -4,3is translated in the same way, what will be its new coordinates?A3,4B1,1C-7,8D1,6

Short Answer

Step by step solution

- Vertex matrix

- Find vertex matrix for points B and C

- Find translated matrix

- Find coordinate of new point

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Calculus

Theoretical and Mathematical Physics

Probability and Statistics

Decision Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

A point is translated from $B$ to $C$ as shown at the right. If a point at $(- 4, 3)$ is translated in the same way, what will be its new coordinates?
A $(3, 4)$ B $(1, 1)$ C $(- 7, 8)$ D $(1, 6)$