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$a. Describe the translation of /_\UTA to DeltaU^(')T^(')A^(') in words. b. Write the transformation rule. c. What is the shortest distance between each image point and its pre-image? Round your answer to the nearest tenth. 6. What are the coordinates of the point (x,y) after being translated p units left and m units up?$

a. Describe the translation of $\triangle \mathrm{UTA}$ to $\Delta \mathrm{U}^{\prime} \mathrm{T}^{\prime} \mathrm{A}^{\prime}$ in words. $\newline$ b. Write the transformation rule. $\newline$ c. What is the shortest distance between each image point and its pre-image? Round your answer to the nearest tenth. $\newline$ $6$ . What are the coordinates of the point $(x, y)$ after being translated $p$ units left and $m$ units up?

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Math Problems

Precalculus

Transformations of functions

Full solution

Q. a. Describe the translation of

\triangle \mathrm{UTA}

\Delta \mathrm{U}^{\prime} \mathrm{T}^{\prime} \mathrm{A}^{\prime}

in words.

\newline

b. Write the transformation rule.

\newline

c. What is the shortest distance between each image point and its pre-image? Round your answer to the nearest tenth.

\newline

6

. What are the coordinates of the point

(x, y)

after being translated

p

units left and

m

units up?

Describe translation rule: a. To describe the translation of $\Delta UTA$ to $\Delta U'T'A'$ in words, we need to know how much and in which direction the figure has moved.
General translation rule: b. Without specific values, the transformation rule for a translation can be written in general terms. If $\Delta UTA$ is translated $p$ units left and $m$ units up, the rule is $(x, y) \rightarrow (x - p, y + m)$ .
Calculate distance using Pythagorean theorem: $c$ . The shortest distance between each image point and its pre-image is the same for all points and is equal to the length of the translation vector. This can be found using the Pythagorean theorem: $\text{distance} = \sqrt{p^2 + m^2}$ . Without specific values for $p$ and $m$ , we cannot calculate the exact distance.
Coordinates after translation: $6$ . The coordinates of the point $(x, y)$ after being translated $p$ units left and $m$ units up are $(x - p, y + m)$ .