Mathematics: What is the composition of the translations (T〈−3, 4〉 ∘ T〈8, −7〉)(x, y) as one translation?

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What is the composition of the translations (T〈−3,

Ответ:

bee1538

06.02.2022

Mathematics

Given:

The composition of the translations is

$(T\langle-3,4\rangle \circ T\langle 8,-7\rangle )(x,y)$

To find:

The composition of the translations in one translations.

Solution:

We know that, $(T\langle-3,4\rangle \circ T\langle 8,-7\rangle)(x,y)$ means $T\langle 8,-7\rangle (x,y)$ is followed by $T\langle -3,4\rangle (x,y)$ .

In $T\langle 8,-7\rangle (x,y)$ ,

$(x,y)\to (x+8,y-7)$

So, $P(x,y)\to P'(x+8,y-7)$ .

In $T\langle -3,4\rangle (x,y)$ ,

$(x,y)\to (x-3,y+4)$

$P'(x+8,y-7)\to P''((x+8)-3,(y-7)+4)$

$P'(x+8,y-7)\to P''(x+5,y-3)$

Now, after composition of the translations

$P(x,y)\to P''(x+5,y-3)$

Here, rule of translation is

$(x,y)\to (x+5,y-3)$

Therefore, rule of translation is $T\langle 5,-3\rangle (x,y)$ .

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What is the composition of the translations
(T〈−3, 4〉 ∘ T〈8, −7〉)(x, y) as one translation?

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