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The translation T maps the point (-3,2) onto (4,3). Find where T maps point (7,4) (b) Two numbers differ by 8 and their ratio is 5:6. Find the two numbers.

June 11, 2026Mathematics

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Answer

\begin{pmatrix} 14 \\ 5 \end{pmatrix}

2 steps

Hapa kuna suluhisho la swali la 15(a):

Swali la 15(a): Tafsiri T inahamisha nukta $(-3,2)$ hadi $(4,3)$ . Tafuta wapi T inahamisha nukta $(7,4)$ .

Tafuta vekta ya tafsiri.
Tafsiri T inahamisha nukta $(-3,2)$ hadi $(4,3)$ .
Hii inamaanisha kuwa mabadiliko katika x ni $4 - (-3) = 4 + 3 = 7$ .
Na mabadiliko katika y ni $3 - 2 = 1$ .
Kwa hiyo, vekta ya tafsiri ni $\begin{pmatrix} 7 \\ 1 \end{pmatrix}$ .
Tumia vekta ya tafsiri kwa nukta $(7,4)$.
Ili kupata wapi T inahamisha nukta $(7,4)$ , ongeza vekta ya tafsiri kwa nukta hii:
$\begin{pmatrix} 7 \\ 4 \end{pmatrix} + \begin{pmatrix} 7 \\ 1 \end{pmatrix} = \begin{pmatrix} 7+7 \\ 4+1 \end{pmatrix} = \begin{pmatrix} 14 \\ 5 \end{pmatrix}$
Kwa hivyo, T inahamisha nukta $(7,4)$ hadi $(14,5)$ .

Jibu la mwisho ni:
$\begin{pmatrix} 14 \\ 5 \end{pmatrix}$