R S T with vertices R(-2,-2), S(-3,1), and T(1,1) is translated by (x, y) →(x-1, y+3) . Then the

Name: Problem 33, Chapter 1: Geometry
Uploaded: 2023-09-11T08:18:49-08:00
Duration: 2 min 39 s
Channel: Jennifer Stoner
Description: R S T with vertices R(-2,-2), S(-3,1), and T(1,1) is translated by (x, y) →(x-1, y+3) . Then the image, R^' S^' T^', is translated by (x, y) →(x+4, y-1), resulting in R^'' S^'' T^'' . a. Find the coordinates for the vertices of R^'' S^'' T^'' b. Write a rule for a single translation that maps R S T to R^'' S^'' T^''

step 1 Here we have triangle RST with vertices of R at negative two, negative two, S at negative three,

Question

$\triangle R S T$ with vertices $R(-2,-2), S(-3,1),$ and $T(1,1)$ is translated by $(x, y) \rightarrow(x-1, y+3) .$ Then the image, $\triangle R^{\prime} S^{\prime} T^{\prime},$ is translated by $(x, y) \rightarrow(x+4, y-1),$ resulting in $\triangle R^{\prime \prime} S^{\prime \prime} T^{\prime \prime} .$ a. Find the coordinates for the vertices of $\triangle R^{\prime \prime} S^{\prime \prime} T^{\prime \prime}$ b. Write a rule for a single translation that maps $\triangle R S T$ to $\triangle R^{\prime \prime} S^{\prime \prime} T^{\prime \prime}$

   $\triangle R S T$ with vertices $R(-2,-2), S(-3,1),$ and $T(1,1)$ is translated by $(x, y) \rightarrow(x-1, y+3) .$ Then the image, $\triangle R^{\prime} S^{\prime} T^{\prime},$ is translated by $(x, y) \rightarrow(x+4, y-1),$ resulting in $\triangle R^{\prime \prime} S^{\prime \prime} T^{\prime \prime} .$
a. Find the coordinates for the vertices of $\triangle R^{\prime \prime} S^{\prime \prime} T^{\prime \prime}$
b. Write a rule for a single translation that maps $\triangle R S T$ to $\triangle R^{\prime \prime} S^{\prime \prime} T^{\prime \prime}$

Geometry

Edward Burger, David… 1st Edition

Chapter 1, Problem 33

Instant Answer

Solved by Expert Jennifer Stoner

09/11/2023

Step 1

Applying this to the vertices of $\triangle RST$ gives us the vertices of $\triangle R'S'T'$. For $R(-2,-2)$, we get $R'(-2-1, -2+3) = R'(-3,1)$. For $S(-3,1)$, we get $S'(-3-1, 1+3) = S'(-4,4)$. For $T(1,1)$, we get $T'(1-1, 1+3) = T'(0,4)$. Show more…

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$\triangle R S T$ with vertices $R(-2,-2), S(-3,1),$ and $T(1,1)$ is translated by $(x, y) \rightarrow(x-1, y+3) .$ Then the image, $\triangle R^{\prime} S^{\prime} T^{\prime},$ is translated by $(x, y) \rightarrow(x+4, y-1),$ resulting in $\triangle R^{\prime \prime} S^{\prime \prime} T^{\prime \prime} .$ a. Find the coordinates for the vertices of $\triangle R^{\prime \prime} S^{\prime \prime} T^{\prime \prime}$ b. Write a rule for a single translation that maps $\triangle R S T$ to $\triangle R^{\prime \prime} S^{\prime \prime} T^{\prime \prime}$

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Key Concepts

Translation in Coordinate Geometry

Translation is a type of transformation that moves every point of a shape or object the same distance in a specific direction. It is performed by adding a fixed vector to the coordinates of every point, resulting in a new figure that is congruent to the original without any rotation or reflection.

Vector Addition

Vector addition is the process of combining two or more translation vectors by adding their corresponding components. This principle is used to determine the overall effect of multiple translations by summing their individual horizontal and vertical displacements.

Composition of Transformations

The composition of transformations refers to the process of applying multiple transformations sequentially. In the context of translations, the overall effect is equivalent to a single translation whose vector is the sum of the vectors for each individual translation.

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